I was able to replicate that separate co-star bug again last night in a battle chest match. I had heard you could be invincible with it but I intentionally went directly into a clump of Oaks to test that and was promptly vanquished. It does seem to be related to using the 'two headed dragon' upgrade as had been discussed elsewhere. If it can be made invincible, it wasn't automatic, but obviously that needs to be fixed.
I've not had any issue with shots registering with the Wizard, but if you do charge his shot, be aware that if you release the button too early, you will fire a normal uncharged shot and waste the time you had put into a partial charge. The charged shot is probably the weakest part of his kit. I can't speak on the auto-shot exploit with specific controller types but it's been reported so much that it's obviously a serious problem.
As we talked about in the battle arena thread, wizards, in fact all new characters, should not be allowed in the arena until we've had time to test them in depth. This is doubly true when ranked is a thing.
The glitching and exploits that I see videos about, Wizard, Imp, Acorn, etc. need to be fixed, and should have been fixed by now. The wizard's ability to ride other characters exacerbates an already bad situation.
Edit: The hit registration issue again sounds far worse on consoles than PC based on what I've seen posted. I see it on PC with melee attacks but ranged attacks doing so are very rare. This is a critical issue that honestly should have been eliminated prior to Founders.