[hunter2_]

I haven't tried cold water so I'm not sure what it's like, but this would be highly dependent on climate. Up north in the winter, cold water is quite cold. Of course, if the pipes go though interior walls for a very long distance through your living space before reaching the toilet, then you'll have a decent temperature unless you flush (or run the sink, etc.) just prior.

"Old work" electrical boxes are specifically designed to be added without tearing apart the drywall (other than making a clean hole, obviously). The lack of romex staples over a fished wire in such scenarios is typically acceptable by code. Now if the bathroom isn't immediately above a basement or immediately below an attic, it might indeed be impossible to avoid some demo.