a) Doesn't a launcher require at least 10 rounds in its magazine? You could of course break with that, but that would pretty much break capital missile launchers to some extent in my opinion. Within reasonable numbers of fighters you'd be down to 2-4 launchers at most. That's workable of course, but won't really save you bay doors unless you only use a single door in recovering them; your launch rate also wouldn't be faster.
I am pretty sure that 10 round magazine minimums are a rules limit, not a technological problem. However, I would also point out that a system like this would have little value on a ship that didn't carry large quantities of fighters. I was also talking about custom ships, not cannon ones. Something carrying 1000 fighters but limited to 30ish bay doors, would be able to install these it greatly increase the possible launch rate.
Also for the record: I was talking about using a single bay door or small number of bay doors to recover the fighters, much like Battlestar Galactica and Babylon 5 do.
b) Missiles are effectively stored as cargo. Units technically need a tech team to ready them after pulling them out of cargo storage. There's of course always the counterexample of the airship carrier that runs cargo-stored fighters through a fighter bay before launching.
Aerospace fighters are also stored as cargo unless they are in fighter cubicles with their own small tech team keeping them ready for use. This idea would attach fighter bays to the launch system. Once the ones in the bays are launched, you could pull more out of cargo and begin prepping them for launch as well.
Perhaps something more custom would work better. Perhaps a combination "launch/recovery gear" that doesn't need a bay door, can launch fighters, but has a certain minimum (or set number) of fighter bays assigned in whose cradles it could also store missiles. Perhaps limited to a certain identical model of fighter/missiles in all its bays? With no reloading from the ship, we're limited to what's stored in there. If you want to limit it even further default to maximum one such system per facing, if you want to tweak it with a bonus over AR-10 optionally add tele-operated missile capability...
Say a 1000-ton piece of equipment that can launch a squadron of six identical fighters or six missiles of a certain type at one per turn. Requires gunners like a capital missile launcher regardless of whether it's used as one. Upside: Saving doors, higher launch rate, missile/fighter launch commonality. Downside: needs crew, tonnage penalty, low flexibility.
There is little reason to design a system that can't reload from cargo. Battletech already does this with both it's fighters and it's torpedoes (and every other weapon you can put on a ship). That limitation makes no sense to me to add. It also wouldn't effect game balance much since it takes a minimum of 15+ turns to prep a fighter from cargo to flight ready, so "reloading" over the course of 15 turns probably wouldn't alter the battle much.
The "One per Facing" limitation in battletech is limited to only three items as far as I am aware: dropshuttle bays carrying two 5000 ton dropships, pressurized and unpressurized repair bays, and mass drivers. These are far too small a scale to be put in the same category. I would simply include these launchers in fire control calculations, so the more you include the more tonnage it will cost you, and possible the more weapons you don't put on in favor of them. This would leave design possibilities more open, while still restricting how many you can have. Each would also definitely have it's own crew, just like any capital weapon, and I wouldn't be opposed to having each launch tube have 2-3 crew.
