1.  Open up the ship's entity file, and near the bottom by the squadrons it can launch there's something labeled CommandPoints.  That is the number of squadrons it can carry.

2.  Yes.

The rate of squadron increase as capital ships level up is also changeable in their entity file.

Be a little careful in adding extra squadrons. Depending on your computer spec, adding too many squadrons can create lag.

Are you talking about the carrier capital ship or the carrier cruiser ?

Most people have 3 or 4 carrier cap ships and 50 to 100 cruisers. Adding a couple of squadrons to the cap ship doesnt do much.

Its usually the cruisers people mod, and so adding 1 squadron to 100 crusier carriers adds a great deal of craft for the program to keep track of and display. Add 3 and suddenly your adding 300 extra entities to the combat. At that point, it can be a lag problem. (Been there, done that).

Adding 4 squadrons to the cap ship actually makes very little difference to combat mid to late game. But adding 1 extra to cruiser carriers makes a great deal of difference (unless you dont actually use them.).