I would like for Starsector to become something akin to a strategy in the late game, except letting me play these battles I find entertaining and autoresolving the rest, but it's not becoming that and there's not much you directly do with your colonies.
1) Yes, if you have blueprints and resources for it. I think that if your colony doesn't it imports them instead, but don't quote me on that. And it will be possible to order particular ships (and weapons? I can't remember) as well.
2) Not without mods.
3) Your faction just does its own thing most of the time. Colonies do make their own fleets and defend themselves, though.