can students whose parents have family passes use it on a school field trip?

Better contact Zoo for that

Short answer yes. Might have to go into the other entrance. But usally they have it in the back as well.

Most of the time the school take care of everything ...but if not the parents have to be there

I think the field trip is free for students.

You definitely are allowed to if the parent is along. I am unsure if the parent is not there.