1. Not necessarilly. Umps want outs...at least in LL.
2. Batter must try to make an attempt to not be hit. Umpire opinion on that. Normally too fast of a pitch so they turn their shoulder. Leaning into a pitch will be a different story.
3. Yes it is if caught.
4. hit by pitch if not swung
5. do not run past that bag on a walk. You are entitled to the base only.
6. Yes, they have plenty of time to move if a play is at the plate. If there is a stolen base going to third, batter does not have to move...let the catcher work around him.
I think I did pretty good without looking at the answers.