Just my two cents.
1. 50% part time. This one is different from the H1B petition position at Univ. A. Mainly, the prevaling wage could be different for full time and part time. So another petition should be ted. But you probably want to check with different immigrant lawyers and the person in charge of H1B in your school to confirm the Memo thing. I don't have any experience on that.
2.B校準備給我單獨辦再申請一份H1B
Not clearly about what you want to say here. If H1b at Univ. B is completely different from the one at univ. A, you probably have to wait till you get the approval notice, instead of receipt, to start working at B. However, if it is a transfer based on H1b at Univ. A, then you can work as soon as you get the receipt notice.
Good Luck.