"to go up in a puff of smoke" and "to vanish into thin air" This is how the expressions are usually said and there is a difference in these expressions. In the first expression there must be a cloud present, be it dust, smoke, gas, etc. The thing that disappears does so in this cloud. In the second expression there is no external cover, the thing that disappears is present one moment and gone the next.

Yes, they mean the same thing. Something disappears very suddenly.

Yes. They both mean the same thing.