Do you have any suggestions if a half inch easy out for removing the threaded portion of a shower head pipe that broke off inside the wall does not work?

If you can access the internal portion of the broken pipe, insert a hacksaw blade and cut through the threads at a perpendicular angle. Be careful not to damage the underlying threads in the pipe in the wall. Then use a flat bladed screwdriver to collapse the damaged pipe at the cut you made, by prying. You may have to make several cuts.