Frozen rusted bolts... removal

True, if you have a tig welder.

However..
If one asks for help in regards to removing broken bolts/studs, I would not assume he has a tig welder.

Worst case if no tig is available..
Use a 90* air drill, extractor, tap to clean it up.
...
Or if you can get a grip on it...torch the head around the bolt, shoot penitrant into it..use vice grips going back and forth as you back it out.