Can you go to jail if you forge a prescription in UK/Ireland for Xanax?

You may not get away with that.  It is not commonly prescribed in the British Isles.

The fact Xanax is an American brand name so that doesn't exist in the UK/Ireland. The drug is not available on the NHS but the class C drug of a branded EU name can be obtained on a prescription from a private doctor, same in Ireland, not sure where you think you could get a prescription form from to be able to forge it

Yes - forgery is illegal. 

In theory, yes.  The chances are that if you required it for your own use, you'd be fined.  If you were a dealer, you'd be jailed.

We don't have Xanax by that name in the U.K.

We also call jail Prison, so you don't live here do you? So the point of your Q is useless.