1) Carriers carry the same number of squads, but the Advent has the best fighter/bomber bonuses (and also the most craft per squadron)
2) There are 4 different types of capitals, all greatly different from one another.
3) Star travel is pretty plainly phase space from one star to another, though yes it is accelerated.
4) The Vasari Kotsura cannon damages everything in the gravity well by 10% hp, while disabling all ships for a short while, and all orbital structures for a long while. The Advent's Deliverance Engine spreads massive amounts of culture, so it's more of a support superweapon.
5) One ship can slow down a group of enemy ships and make them unable to phase jump. Another can restore a good chunk of shields to all friendly ships near it. Another can make fighters/bombers crash into the target ship, dealing damage. One can do heavy damage to another ship/structure while repairing from it at the same time. Of course, one of the favorites is the planet sucker! Forms a massive vortex that literally sucks the planet, damaging it and giving you resources in return. Another race has a similar concept, except it just causes a panic that makes people kill each other

6) Light carriers are cruiser-sized and have no weapons. Like I said, they carry one squad, but the mobility of fighters/bombers makes them very useful.
7) First you bomb, then you colonize with a colony ship (or, each race has one capital that can colonize)