You have a few options.
- Influence. I've never done this particular scenario to test that this works for this scenario, but in general sandbox games it's an option. Once you have all their ships dead, build influence bases until their planets flip.
- Sequential invasion. Send one transport at a time to invade. Using 1 billion troops per transport, you *should* be safe using mass drivers on any planet over 10-12 billion (will vary on situation, save before testing). The trick is, if you invade and fail, the planet quality doesn't drop from the invasion tactic. Send one transport in, blast them good but lose, then mop up what's left with another transport or two.
- Swamp them. If you have tidal disruptors, use them. They become more effective as your opponent's soldiering ability increases.
- Sabotage morale. If their planets are pretty crouded, slap some spies on any morale buildings on the planet, then invade with information warfare. Some of their troops defect to your side, increasing your troop count and decreasing theirs at the same time. It is quite possible to end an invasion with more troops than you started with using this tactic.
- Zerg rush. Build lots of tiny hulls with advanced transport modules on them. They'll take a while to fill without depopulating your planets, but once you can put 15 or so of them in a fleet at one time, you can crush pretty much anything. If you attack with transports in a fleet, some of the transports can survive to be reused. Specifically, as many will survive as how many troops you end the battle with, rounding down. If you attack with 15 transports @ 1 billion each, and live with 10.3 billion troops, 10 of the transports will survive for reuse. Even if you use the morale trick above, you will always lose at least one transport per invasion, even if you end with enough troops to fill every transport you brought.
As for specific questions:
NO! If you win an invasion using an invasion tactic that damages planet quality, the damage cannot be repaired. Tidal disruptors are particularly good to use, as they will destroy buildings but not damage the planet quality. Information warfare and standard invasion (no tactic) will not damage buildings or quality, but you may lose buildings you don't have the tech to build.
There is a way to estimate how big your force needs to be. Attack with one transport and look at the "advantage" number you roll when you invade. The number of troops involved doesn't really matter, but the ratio of your advantage to theirs determines losses (roughly). So if your single transport attack gets a roll of 11 to their 23, you can estimate a 2:1 troop superiority will be needed to break even against them. Do keep in mind it is a fairly crude estimate - your next roll could do better or worse, so include a generous safety margin in your calculation. This estimate will change depending on the invasion tactic you use.
