I'm a little surprised to see this on the GC 4 forum. No matter. I'll answer GC 3 questions.

I think a limit of 1 Military academy per player is one of the bad decisions stardock has made for this game. I recall that it was unlimited back before retribution. I think stardock thought that players should rely on supply ships to feed worlds with military academies and tech capitals. Military academies allow you to produce legions, and tech capitals allow you to aid research.

You can capture planets with these planet improvements to add to the list of what you own.

I prefer to manufacture legions as I rather turn my citizens into leaders. Its expensive I know. I would avoid trying to capture homeworlds as the AI likes placing generals on those worlds. As a side effect, each general allows up to 5 legions to double as a garrison on affected worlds, so they're going to be defended.

Overall, you want to avoid capturing worlds with garrisons as they will kill some of your legions and the fighting may damage the planet. Instead consider paying someone else to finish a civilization off. You will have to deal with them later, but you don't have to worry about as many garrisons.

Also defend your troop transports. They're not as easily replaced as they were in previous titles. On the plus side, you shouldn't need as many.