Those mirrors are hard to get to. Posslble answer to your loose arm is: hold tension and unscrew at the same time. Rivet arm to piece of Al. and glue back on plywood. That does not solve loose frame. There are rivets in the frame that must hold the mirror together. If removed ,would that open a can of worms?? One solution to whole problem may be to cut a piece of al. the full size of the frame, clamp to frame, mark holes of arm, rivet arm to al.,then glue entire al. to back of plywood and hold with clamps. Clamps that I have found useful are the spring clamps that hold paper together available at Staples. Don't know where to get al.???
Tom