If you can hold the idea of an omnimax god in your mind's eye, then you've got a better imagination than I do.
I can individually comprehend the meanings of all the terms used to describe such a god, but not the thing as a whole. In this regard, it's exactly the same as a square circle for me.
Hmm. It's hard for me to say what would be the best term to avoid confusion, since I'm still not entirely sure of what you're going for with "existence".
And then, if they think it through, they'll realize that the existence of God implies the existence of existence, and that even God can't "create" something that already exists.
I'm actually just trying to figure out what you mean. So far, I haven't gotten the sense that your original question is anything more than a bunch of impressive-sounding terms thrown together.
So then, if I propose an infinite that conflicts with your idea of the infinite, you'll accept it without asking me for evidence?