Also do they start taking people off the waiting list before hearing the appeals or do they have to wait until the appeals are over?
Other way around.
As soon as places are declined after March 1st, they will start offering places from the waiting list. They might wait at first until they've got enough spare places to offer all the children with equal ranking a place, so do it in steps.
They can, and do, carry on offering places from the waiting list until the school / admissions authority are given the list of successful appeals once the appeals are complete. Then they will have to wait until the role is back to the Indicated Admission Number before the waiting list moves again.
The two processes are separate and work in parallel. On the panel, I have known appeals that we've already heard be withdrawn as a place has come up for that child in either the school the appeal is for or another school they were waiting for. We know nothing of position on the waiting list - we do know the score of the child but that does not necessarily mean that they are on the waiting list!