1. Not that I've found, at least not without a mod, but I wouldn't suggest getting into that yet.
2. Yes, as long as there is no Culture Center in the gravity well, just leave a capital ship (they repel culture) in the system and wait until you can colonize it, or destroy whatever Culture Center nearby is spreading the culture, and again wait for culture to clear from the system.
3. For Advent, TEC, use a Colony Frigate, they have a Capture ability for neutral asteroids. For Vasari, the Scout Frigates have this ability.
4. The color of phase lanes represents the hostile culture, that is the reason you cannot colonize them, when the color in phase lanes near the planet has receded to the planet you can colonize it.