Letter of Recommendation/Reference Protocols
Yes. It's quite typical to ask each prof to write a letter for each school you apply to. Indeed, you almost certainly want to do this. Be sure to take care of all the paperwork beforehand, pre-address envelopes if any applications use snail mail, etc. so he/she doesn't have to. 
No. 
Hard to say. I'd find someone else in your department (who knows the prof in question) to ask. Good luck!