Good questions!
- Stand in the face of danger is about choosing whether to attack or defend against a threat. So if you pick the 1st 10+ option ("Stand firm and nobody gets hurt"), you can defend yourself and others, but you won't necessarily lash out against the threat. This is useful if you want to take a nonviolent course of action, or if you need to protect someone else. If you choose the 2nd 10+ option ("You aren't hurt, and you hurt the threat right back"), you're deciding to respond to a threat with aggression, and you may not be able to protect others (even if you're okay).
- Learning a spell is supposed to be fairly easy, but it still requires a character to find the information in-game. You need to locate the correct book, seek out an instructor, etc. The advancement option handwaves this process and allows you to know the spell immediately. The luck point option allows you to, in an emergency, attempt a spell you haven't learned at all. Of course, if you want to play a character who hauls around forty textbooks around at all times and stops the action to spend 15-30 minutes reading a book to learn a new spell, there's nothing in the game rules that says you can't.
- Yes, "Offer them 1 Experience to stop what they're doing" is just between player characters. So it's a negotiation between players, and they're free to work out what that looks like narratively between themselves.
Hope that helps!