Whatever you paid in ore to get the building built will come out as waste when you demolish the building.
Happiness is a measure of how much the people are behind you when it comes to colonizing other planets. Without this backing your people simply aren't motivated enough to explore outside their known world. There is no cap to the amount of happiness you can accumulate on each planet, and each planets happiness is independent from the others.
Waste is the excess produced with any kind of production. Used wisely it can be a valuable resource that can be turned into other needed resources. Used poorly it can turn into pollution that will decrease your empire's happiness. Without happiness you will be unable to colonize other planets.