With regard to "warping" the language to make a point about God: one doesn't have to involve "God" to highlight the limits of language or our inability to resolve some apparent contradictions. Quantum mechanics does a nice job of it on the physical-sensory level (Level 1); and (eg) the Omnipotence Paradox does so on the mental-symbolic level (Level 2).
When encountering an apparent contradiction, you can come to one of two conclusions. Either you accept it as being "only apparent," as well as accepting our limits to adequately resolve it (as on Level 1); or you regard the contradiction as genuine, one which proves that the phenomenon in question ("omnipotence"😉 doesn't exist.
As for defining "God" or "proof": any substantial philosophical discussion dictates that terms be agreed upon beforehand, otherwise you and the other guy could be talking about (if on a very subtle level) 2 different things.