From my personal experience (from school to school):
1. The first day you work for the new school is the day you get the receipt notice of your application for new H1B from BCIS. This day is the day you can have the salary from the new school.
2. During H1B pending, you should be able to keep your status legally.
3. After your H1B is approved, you can tell when your old H1B is end by the new Valid date in your new H1B. This is just my personal understanding.