The story is phrased in a way that is delicately subtle, and thus elides the mechanism whereby the drunk can change his rotation.

Here's a hint: It's relevant that the person is drunk. Another hint: Newton's third law.

I call it my inbuilt vectoring urea reaction engine.

Since you're the only thing in this hypothetical universe, you better make sure your urea makes it to escape velocity (which shouldn't be hard), otherwise you'll make it rain.

No, because angular momentum is conserved, assuming flat space. It is possible to change one's orientation, however.

Yes. He can use the gyroscopic effect of his head spinning.

You could blow in one direction or the other, at an angle. The air you push away will push you the other way.

If you're suspended in a fluid or gas, you're not in a void.

Well, if he had a lungful if air, blowing would work - after all, rockets do work in a vacuum.

That said, he’s drunk, so the answer is to piss into the luminiferous aether.