What would a helicopter do in space?

Nothing. There is no air for the spinning blades to move and create the high / low pressure system that gives the helicopter lift, it would not move unless acted upon by an outside force.

The cockpit and the blade would spin equally fast, but the craft itself would never go anywhere because helicopters push air to move, and there is no air in a vacuum

leak air rapidly so the crew would die

spin around in the opposite direction to the rotor, as the tail rotor would have nothing to push on. Of course the engine would not work in a vacuum, but suppose you had a toy electric one launched out the airlock...

Nothing unless acted on by an outside force

It would float around like any other piece of space junks.

It would copter around in the intergalactic wonders of the never ending darkness space.

Not much but drift around. combustion engines can't work when they get no air.

Write in the sky:"Josh is an imbecile".