1). After you have researched the first level of Terror Stars, you may have a constructor build the base of a terror star. Each additional technology allows another module (maximum five or so, I think). After you have a terror star, it will still be useless for ten turns or so while it becomes operational. After that period, you will have an overpriced, slow-moving weapon that will nonetheless be so awesome that it will allow you to crush your opponent's face underneath your iron heal. "Surrender, foolish mortals!" it will cry in the language of power, "Know that you are inferior. Know that you are dead in your impending death. Know that you are at the mercy of a merciless universe." All things will wither, flame, and die, and the lifeless universe will echo with the memory of death.
2). You cannot actually lower maintenance to the best of my knowledge, but there are a number or things to help early expansion. The most important is to pace expansion. That extra planet is worthless if it will prevent production on any of them. Keep an eye on morale and taxation for population growth. An early focus on morale, population growth, or economic technologies is not a bad thing. You can always take those bonus points if you are having serious troubles. Watch whether you are building, buying, or leasing your colony ships. All of those options have their uses. I would advise avoiding leases until you know how to use them (which, personally, I don't really know) because otherwise they are just another tool for you to kill yourself with. In any emergency, simply drop production and raise taxation to any point where you are still gaining population. Gaining population is the important thing, people are money. If you want to try a race with an easy colonization rush, try the Torians. If you want to est an extreme example of a difficult colonization rush, try the Drath.
Also, if you are playing on tiny or maybe even small, four planets may not be too bad if they are high quality. Any larger size and there are problems
3. Nothing very useful.