Miscellaneous Starship Problems
The meaning of "NCC" Matt Jefferies allegedly modified the registry of his airplane (NC-17740) when he devised the number NCC-1701 for the USS Enterprise. Anyhow, "NCC" was never supposed to have any specific meaning apart from being a generic prefix for Starfleet registries. The suggestion that it should be an abbreviation for "naval construction contract" is popular in fandom, but mere speculation and therefore non-canon. Since other Federation prefixes include "NAR", "NCV", "NFT" or "NSP", it is much more likely that the leading "N" denotes Federation starships. Only "NX" could stand for something specific like "experimental", but there is no real evidence either.
NC-17740 @ Virginia Aviation Museum
The meaning of "USS" While "USS" was definitely supposed to be reminiscent of "United States Ship", the abbreviation was meant to denote "United Space Ship" in the early stages of the Star Trek production. Christopher Pike explicitly stated this in "The Cage". Later on, it was switched to "United Star Ship" which James Kirk mentioned at least at one occasion in TOS: "Court-Martial". There is no problem in accepting both versions, since the official nomenclature could have "promoted" all space ships to starships some time after the 2250s.
The ships of 22nd century Earth Starfleet don't have name prefixes, at least they are never referred to in spoken or written form. There is only one exception. In ENT: "Divergence" we can see a display on which the two ships are labeled "USS Enterprise NX-01" and "USS Columbia NX-02". While "USS" may stand for something like "United Sol (System) Ship" here, we are probably allowed to ignore this one-time exception.
The meaning of "explorer" or "frigate" Starfleet ship types are occasionally referred to in Star Trek episodes. For instance, a screen display in "Star Trek III" (actually reproduced from the Star Fleet Technical Manual, see here) identifies the Enterprise as a "heavy cruiser". In TNG: "Arsenal of Freedom", the Wambundu class is supposed to be a "light cruiser". In TNG: "Conspiracy", the Ambassador class is called a "heavy cruiser" and the New Orleans class a "frigate" (although none of them is shown). The Defiant is classified as an "escort" in DS9: "The Search". "Destroyer units", finally, are mentioned by Ben Sisko in DS9: "Sacrifice of Angels". All this points to a classification system quite similar to that of present-day navies, where the designation primarily stands for the ship's size and armament. The TNGTM, on the other hand, does not mention military designations. According to the book, the ship types denote specific roles, rather than sizes: "The USS Enterprise is categorized as an Explorer, the largest starship in a classification system that includes cruiser, cargo carrier, tanker, surveyor, and scout. While most starships may be adapted for a variety of mission types, the vessel type designations describe their primary purpose."
Whilst there is no problem with all the auxiliary vessels like tankers or cargo ships which are just what their name says, the question arises what may be the difference between all the "military" designations, also considering that Starfleet is just not supposed to have warships (DS9: "The Search"). The navy classification system may be used only as a matter of tradition. But, in particular, the designation as "explorer" exclusively for the largest type makes little sense, as this is the primary purpose of all capital ships. "Explorer", as a new term probably replacing "battleship", says nothing about the ship's size and doesn't fit into the naval classification system. The entry in the TNGTM is also somewhat contradictory in itself in that it states that the explorer should be the largest ship type, although size wouldn't matter in a classification by primary purposes. The difference between explorer and cruiser is not made clear either.
It has been conjectured that, since the designation as a frigate and the distinction between heavy and light cruiser is missing in the TNGTM, there are actually two parallel type designations: one for the ship's (peace time) role and, optionally, an additional "military" type for the ship's size. According to this theory, the Intrepid class, as a vessel fully equipped with all kinds of weapons and with sensors and labs for long-term exploration, may be an explorer (as the ship's designer Rick Sternbach once suggested), just like the much larger Galaxy class. The Sovereign class, which many fans do not want to accept as a heavy cruiser, although it is smaller than the Ambassador class, may be an explorer likewise. A dual classification system would also allow the term "battleship" to be still in use, as TNG: "Conundrum" suggests where the Enterprise, albeit under amnesia, is identified as "battleship". But especially "destroyer" and "battleship" would not suit an organization at all that takes pride in the peaceful exploration of space.
While it may explain everything stated on screen as well as in the reference books, there is no evidence for a dual classification system. Considering the minor role that these designations use to play in Starfleet, a second one for many ships appears to be superfluous. It may suffice to agree that the largest fully equipped ship type is called "explorer", although smaller ships are used for exploration too. "Heavy cruiser", "light cruiser", maybe "destroyer" (although the mentioned "destroyer units" do not have to be designations of ship types) and "frigate" are essentially gradually downsized explorers, and there are no battleships or battlecruisers in Starfleet. "Escort" may be an extraordinary designation, as Starfleet couldn't fit the Defiant, which has no specific role except for fighting, into their scheme. All support ship types are just called what they are used for.
I suggest to take this question easy. Even in present-day navies the designations may be subject to change, as new frigates are often larger than destroyers, and the latter seem to come out of use anyway. In many cases Starfleet probably doesn't know itself how to categorize a new ship class, just like it was with the Defiant. I wouldn't know how to classify the Prometheus, and please don't ask me about the Saber, Steamrunner or Norway either. There is absolutely no clue. Making up terms like "fast attack frigate" or "strike cruiser" and insisting on them is fanboyish and unbecoming of Starfleet.
The size of Starfleet There are several different approaches to determine the overall number of Starfleet ships. First of all, the registries suggest that some 76,000 starships have been in service between 2161 and 2376. We can't be positive that the numbers are actually strictly chronological, and we don't know how many ships are or were in service at a time. The mere numbers would easily allow 30,000 ships. Anyway, the careful assumption that there are rather several thousand than a few hundred starships should be possible. The fleet sizes of the Dominion War are more obvious evidence for the size of Starfleet. If there are at least nine fleets with around 200 starships each, we obtain a few thousand starships.
There seems to be a dilemma if we compare the high registries and the huge fleets of the Dominion War with what seemed to be a chronic lack of ships in the times of TOS and TNG, where the Enterprise was on its own most of the time. The whole issue, however, has to be assessed completely differently if we further consider the popular setting "We are the only ship in the sector / within reach", as it was the case several times in TOS and TNG. A sector is supposedly a cube of 20^3 light years, and traversing a sector is possible with a fast starship in a few days. If the Federation is a sphere of just 200ly diameter, its volume is 4.2 million cubic light years. This is still a lot, in spite of the seemingly small diameter, and it would equal 524 sectors. We would have to take into account that certain sectors in the center of the Federation and at the Cardassian border, for example, would be "populated" with more starships than sectors of lower logistical or strategic importance. This makes it very plausible that the Enterprise is sometimes the only starship in a remote sector if there are a few thousand ships altogether. If we like a larger Federation better, the starship density would be even thinner than it was suggested in TNG. The explanation why suddenly large fleets appear during the Dominion War is simple if we take into account that it is only a matter of a few weeks to assemble such a fleet from the ships in neighboring sectors. There was just no time in TNG: "The Best of Both Worlds" and "Redemption" where the Federation tried hard to gather 40 and 20 ships, respectively.
Families on Federation starships We know that, at the time of TOS, it was not customary to have families on Starfleet ships. At least there were definitely no families on the USS Enterprise. It is possible that research vessels, especially those not belonging to Starfleet, may have had accommodations for spouses and children of ship officers. But this is only speculation. Some time in the 24th century Starfleet may have admitted families to certain ships. On the Enterprise-D this seemed to be a new experience to some of the crew, especially to Picard who was unfamiliar with the presence of children (TNG: "Encounter at Farpoint"). There is no good evidence on families on other Starfleet ships of that time except for the Saratoga as seen in DS9: "Emissary". Ironically this Miranda-class ship is a very old design by the time of its destruction, and we may presume that more recent ship classes of the cruiser type would be more likely to have families aboard. On the other hand, the Saratoga may just have been an exception, a science vessel that accidentally dropped into the battle, considering that there was even a transport ship with civilians at Wolf 359 (mentioned in VOY: "Infinite Regress").
Hull colors The hulls of many Starfleet ships, most obviously of Enterprise NX-01, shine as if they were made of bare metal, something like the future equivalent of stainless steel. Some close views of the hull, like in ENT: "Minefield" seem to corroborate this notion. On the other hand, in ENT: "Broken Bow" Archer says to Trip Tucker, "You scratched the paint", after a minor collision of their shuttlepod with the ship's hull. It looks like the pod could have touched the "X" of the ship's registry, which is quite obviously painted on. But it is also possible that the ship is actually coated with a protective paint that includes metallic particles. This would also explain why there is more contrast between the hull panels than surfaces of the same bare metal likely have. As there is no physical model of Enterprise NX-01, anything is possible anyway.
But the hulls of the starships using physical models are just as hard to assess. This is because the miniatures are painted in a way to look good under studio lighting conditions, rather than at normal daylight. The models of the Galaxy class, for instance, are painted in rather odd shades of gray and greenish gray, while they look almost perfectly metallic on screen, especially in the later seasons of TNG and in "Generations". The model of the Enterprise refit was reported to be plain white by visitors of exhibitions, but may actually be painted in different shades of gray close to white with different reflectivities. This too is supposed to give us the impression of a metallic surface.
Ships without deflectors The navigational deflector is an essential component of every Federation starship, as it is necessary to prevent interstellar particles from hitting the hull (as explained in the TNGTM and stated by Malcolm Reed in ENT: "Broken Bow"). But why are there certain ship classes, like the Miranda or the Constellation, without a deflector dish? A possible explanation lies in the TNGTM where the deflection system is described as consisting of two components: a low-power field to sweep small particles and a focused beam to deflect larger objects such as asteroids. It may be useful to integrate these components into a dish, together with the long-range sensors, but it is not necessary. I could imagine that an almost unnoticeable forcefield generator may be used to keep small particles away, while a phaser-like emitter or even the phasers themselves may take care of asteroids. So the Miranda and Constellation do have deflectors, we only don't know what they look like exactly and where they are located.
In Star Trek: The Magazine (January 2003), Rick Sternbach suggests that the deflector grid, Bussard collector fields, tractor emitter and asymmetrical warp fields are working together to protect the hull on the Constellation. Whilst this sounds very complex compared to a dedicated deflector system, it is plausible if we look at the possible roles of the single systems. We may assume that the shields and warp field disperse small particles, while the Bussard collector can cut through this field combination to collect stray hydrogen. The tractor beam would be used to deflect larger objects.
As opposed to Federation starships, almost no alien ship designs seems to have deflector dishes, even those with similar warp nacelles. This is more evidence that there are other possible configurations of a deflecting system than a dish.
Interstellar travel on a shuttle The usefulness of shuttles is questionable if their maximum speeds are Warp 4 for the Type-9 shuttle (VOY: "Resolutions") or only Warp 2 for the TNG standard shuttles of Type 6 and Type 7 (according to the Star Trek Fact Files). An interstellar journey would take months or even years with such a sluggish spacecraft. We may also remember a few occasions where even the good old TOS shuttle (TOS: "The Menagerie I", "Metamorphosis", "Let That Be Your Last Battlefield") or the Type-15 shuttlepod (TNG: "The Mind's Eye") were used for this purpose - both were intended to have only impulse drive. The authors obviously haven't given the shuttle issue much thought. Maybe they just assumed that any speed faster than light would do, and that everything with something like a nacelle should be warp-capable. The same problem exists with the countless alien and civilian freighters creeping through the galaxy at low warp or even sublight speed. I wonder what else aside from fuel and supplies for the crew such a freighter would be able to carry, not to mention the endless boredom on a journey that may take decades.
In some cases it may be argued that a shuttle was dropped by the ship at the edge of a solar system and made only the rest of the travel alone. Nevertheless, it's hard to deny that shuttles are actually used to travel through interstellar space in some other cases. In some specific cases shuttles even managed to catch up or keep pace with starships, like Chakotay did in VOY: "Unity". This is why I think that shuttles are much faster than is usually stated.
Thanks to Jeff for the hint about the scratched paint on the NX-01.