One of the two screws that fastens the toilet to the group broke on my toilet. The problem is part of the screw is still in the cement. How can I remove the broken portion from the cement and make repairs so the toilet will stop rocking/wobbling. The screw may have broken due to the rocking/wobbling

Unscrew the other screw and remove the toilet. If your screws are set into closet ring, than remove the broken screw. Insert new one, use new wax ring and reinstall toilet. If your broken screw is indeed set into concrete slab, than either drill it out or drill right next to it. Insert new screw into bit of epoxy, let dry, and install your toilet.

If your toilet rocks than use wedges to support it on loose side and caulk with silicone around the base. Let dry overnight.

A screw called a Tapcon does a very good job of holding the flange down to the concrete.