1. To “not let something stand” means to fight back against an unacceptable situation and try to change it. Example: “The government has just passed a law that takes away our liberties. We can’t let that stand.”
2. “Have some of that” (or “take some of that”) is something a person can say after attacking an opponent. “That” is the attack, damage, or abuse that your opponent is being made to suffer. It can also be used in non-physical contexts, like a chess game: You put your opponent’s king in check, and say “take some of that.”
3. It depends on context. The speaker may believe there are aliens and is simply saying he/she is eager to see them, or he/she may doubt there are aliens and wants to see whether or not they are really there.