Plastic surgery, oddly enough, contains no plastic.
The word "plastic" in plastic surgery refers to plasticity - the ability of an object to be reshaped or reformed.
Quite possibly. I think we'd just call it 'automated plastic surgery', though.
There'll be a booth on every street corner, just like phone boxes. Just swipe your phone to pay, then design a new look, or choose from a list of 'looks you might like'. Minutes later you'll be a new person...