Why omnipotent is a paradox.

This sounds sensible but it's too simple and makes assumptions about things that are, by definition, outside what we can know about.It sure isn't going to convince any believer. For one reason it's too abstract and much better logic with much better evidence doesn't convince them of anything.Lot's of luck.

That proof is very specific to mathematical systems with specific properties (Rrhein can give you all the details (perhaps more than) you want. I don't think there is anyway you can justify carrying it over into other areas.So it isn't a valid basis for this "mathematical" proof.

Omnipotent is totally powerful. Omniscient is all knowing.

I think you're right that applying Godels theorem out of place is silly. It applys to mathematical systems not universes as far as I know.

Is God included in anyone?

Then you've gotten to the point that God isn't omnipotent. The term is very strict in it's definition.Here's a defintion:
Having unlimited or universal power, authority, or force; all-powerful.So it's pretty black or white.If God isn't then, omnipotent, the interesting question, for those so inclinded, is where are His/Her limits? That'll keep them counting angels for years.