Regular carriers probably carry a small number of Marines--a company or less unless they are on an assignment that calls for more (such as End Run, where they crammed as many onto the Tarawa as they could). One of the innovations of the Midway class is that it is designed to permanantly carry a full batallion at all times.
Well, it would probably be better to have separate ships for heavy engagements where loss of your carrier was a distinct possibility, but the concept behind the Midway was that it could do the job of an entire Carrier Group for lighter duties--during intense warfare it would normally be escorted by a pair of Plunkett cruisers and several Murphy destroyers and Pelican transports. The main reason that the Midway operated alone in Prophecy is that it was on a shakedown/training cruise and reinforcements were days away--you notice that it is assisted by the Eisen carrier group later in the game.
Launch tubes are meant for launching fighters as quickly as possible, which is what you need if you are trying to intercept an incoming flight of bombers. I don't think that SWACS/Marine LC need to launch in quite that much of a hurry--boarding a ship that you do not intend to capture, as in Fleet Action, is a rarity.
I do believe the Marine LC does in fact use a launch tube... When the Midway is under attack during the convoy rescue mission (don't remember which series, but it's the mission with the TCS Redeemer)and is unable to launch fighters due to sustained damage, the CAG asks Rachel to get the "Marine LC backup" online.
I think the launch tubes can launch Marine LCs. In fact, I don't remeber any official source saying what can or can't be launched by the tubes, or even saying what is a tube and what isn't, this is something we figure out by noticing the gameplay. Of course I might be just wrong about this.
The Marine LC doesn't seem much wider than a Shrike or Devastator. It might be longer than the Devastator but its been a while since I've played the game. Even if it wasn't any larger than a Devastator not needing a massive powerplant to run weapons, computer sytems, and shields and minus the weapons bays would free up a lot of room for personnel. So I don't see any reason they couldn't luanch the LC via the launch tubes.
There is probably a larger craft of some type if the Marines were planning to combat assault a planet. That probably does use the rear bays given its possible size. Besides, it makes sense for the rear bays to be that large if you would have Marine craft on board that would make some use of them. None of the Awacs or shuttles is that wide or high. Just conjecture on my part though.