I would caution you to make sure you identify which god you're referring to. Virtually any discussion about the nature of "God" or "gods" must establish their starting point. Even most theologians miss this part. They instantly assume the debate is starting at a common point not realizing that they flew right past point A and are starting the debate at point C or D.

Are we talking about the Western concepts of "God" that stem from Deist & Epicurean philosophy that separates the supernatural (up there-ness) with the natural (down here-ness) where everything must be either God OR us?

Are we talking about the Hebrew, Earliest Christian, and Eastern Orthodox concept of God that is involved in every aspect of nature (evolution, birds migrating, etc.)?

The question of "Can God make a rock so heavy that he couldn't lift it?" really depends on the starting point. In a Western context, I suppose most would use Lewis or some other rational common-sense answer (i.e, God created all things and is not limited to but has chosen to limit himself to work within the cosoms that he's created). Since creation cannot stand above it's creator, God can be limited to his own laws and still be omnipotent.

In the Eastern context, I would guess that the question would be met with, "When I see God, I'll ask him."