My DD went through this stage and DP was always more successful at changing her when she was being really wriggly. He put his left forearm across her torso and change her that way. I didn't have the upper body strength so it was harder for me. The best I could do was hold both feet in the air in one hand and then try to swipe her butt with a wipe as she wriggled past. I would only lay her down for long enough to clean her up then stand her up to put her nappy on. For the record, pull ups are not easier than nappies when the child is lying down. They don't slide easily and are quite snug. If you do want to try pull ups, get the huggies ones that you can split down the side and reattach. That way if they aren't going on easy you can treat them like regular nappies.
As for biting. I have dealt with some notorious biters and my favourite trick is everytime they bite, keep completely neutral and hand them a chew toy saying "you can chew on this toy, it will feel nice on your teeth." or "this is for chewing." and stick it to their lips. It can take a lot of persistence but pays off 9 times out of 10. Biters are either doing it out of frustration, or because they lack communication skills, or because they get a fun reaction or because they are looking for oral stimulation. Addressing the issue that causes it will emliminate the problem.