When the question(s) "Is there a god?" or "Do you believe in God?" is asked, we learn something about people, but little or nothing about 'god'......

True, because essentially what you're asking is about people: their belief or lack thereof in God.

A question about God, such as, "what is God like?" is a horse of a different colour. That said, the problem with that question is that its answer depends on a host of underlying assumptions that are not universally shared. Add to this the fact that most people don't even realize the underlying assumptions they hold that give rise to their answer to that question, and it does look very subjective indeed. I would not deny this. Further the type of evidence (there's that word again) which underlies most people's belief in God (those that have belief in God), is largely (but usually not entirely) of a subjective nature.