Invasion tactics: I'm pretty sure it makes the tiles totally unusable.
Manufacturing Capital: As per the devs, it's supposed to work that you can only build one, but any that you capture will still work for you. What I've seen in practice is that if you gain one and haven't already placed your own, it won't let you place one.
Population: Population is in Billions. And on a related note that is also wrong, a megaton of food feeds a billion people for a week, not a million.