Hi, I read that you have to give your passport for a week or two once you are in China so
they can convert your Z visa and apply for the residence permit.

But everyone says not to give your passport to anyone or they can blackmail you since they
have it now and you don't.

Is it really required to hand over your passport and be at a school's mercy, or how will I
get the residence permit?

New rules/system introduced a few months ago means that the PSB now needs 20 days to get your visa - though I have no idea why.

Essentially, you have no choice. I assume you would be handing it over to the FAO of your school? Take photocopies of it before you do, and if you're not too comfortable, ask your FAO for a receipt. That's the best advice I can offer you. It's the 'system', I'm afraid!