Yes, they can take the SATs several times and a school will typically look at the highest score (usually that is the last score because you assume the kids get better as they go along). I dont' know what other people think but I wouldn't suggest taking the test more than 2x--maybe 3x maximum. Admissions offices are weird about that (I worked in one briefly at a college in MA.). If you take it too many times you risk having scores all over the place (some high, some low) and then it becomes useless really as a gauge.

I'm not sure if there are "trick questions" but there are definitely certain strategies you can learn to sort of game the system, so to speak. There are all sorts of books with practice exams in them that are old SAT tests--usually the books will give advice on how to approach the questions. Some students will take an SAT preparation course but that can get expensive. Good luck with everything!