I find this post very interesting, but I disagree with your examples about God. This comment is rather lengthy, and rather off-topic, so I apologize, but I wanted to bring it up because your post features these questions so prominently as examples.

Specifically, I don't think that the answer to the questions about God can be written off so easily as "no". It seems to me that the questions "Could God draw a square circle?" "Could God create a stone so large that even He could not lift it?" are asking about the bounds on omnipotence.

Suppose an omnipotent being exists in a universe, and that universe operates under some fundamental laws that among other things define what can exist vs. what is a contradiction. It seems fairly obvious, based on the standard definition of omnipotence, that the omnipotent being should be able to do all things that do not violate these fundamental laws and cause a contradiction. I'll call this Level 0 Power.

"Could God draw a square circle?" is asking about what I'll call God's Level 1 Power. It is asking "Does an omnipotent being have the power to change the fundamental laws of the universe?", or, if you like, "Can God reprogram the universe?" If God is in charge of the rules, then presumably he could rewrite them such that things which are currently a contradiction are no longer a contradiction. In terms of the circle/square question, this seems kind of silly, since circles and squares are not contained in the universe but are products of formal systems invented by humans. Alternatively we could ask "Can God make 1+1 add up to something other than 2?" and the answer is "Of course; even mathematicians can do this, by redefining the axioms or working in the integers (mod 2) or something." In terms of this example, then, Level 1 Power is asking "If the universe is a formal system of sorts, can God change the axioms?"

Suppose God has Level 1 Power and can change the axioms of the system (or systems) he creates. This isn't so hard to imagine; it's like a human programmer rewriting a piece of the code in the middle of running a simulation. But the question about whether God, if he existed, actually had such a power, seems like it would be a reasonable subject of discussion for theologians.

"Could God create a stone so large that even He could not lift it?" is yet a more difficult question. Is it asking about God's Level 1 Power? I think it depends on where omnipotence comes from. If God is omnipotent within the system because that's the way he coded it, then it is asking about God's Level 1 Power: all he has to do is go into the code for the universe and change the part that says he should be able to lift all stones. But if God's omnipotence is something that exists independent of the system, then this question is asking whether God can change the rules which define himself.

Anyway, your answer of "no" to these questions indicates not that the questions are worthless but that you assume an omnipotent being could only have Level 0 Power.