We hang radiators on walls very regularly using toggle fixings, as said below if you can hit a stud that would be class but if not toggle fixings is the way to Go.
Maybe but I have used them a lot over the years on loads of things and as long as you dont lean on them they are usually sound. If your really worried about that Id cut out a section of wall and put a wooden strap/piece of ply in the back and piece it back over.
We hang radiators on walls very regularly using toggle fixings, as said below if you can hit a stud that would be class but if not toggle fixings is the way to Go.