Dont let the mesh plaster or other details keep you from getting the bath you want. At a certain point it is far easier to completely strip the room and start over. About one day of demolition instead of a week of working around problems. Once everything is out: (finishes, fixtures, walls) you have the opportunity to inspect plumbing, install insulation, improve heating, lighting and update electrical to GFCI and so forth. Then it is a matter of putting things back together the way you want them.
From your post, I don't see anything you are intent on saving, and completely stripping the room is more time and cost effective than picking at the things you don't like. A complete renovation will take several weeks. Fixing what is there will take years to accomplish a piece at a time.
Best of luck and I'm sure there will be other ideas.