The Nature of Deity

In my time commenting here, I have often found in a situation where I felt like I was playing the role of Heracles fighting the Lernaean Hydra without a torch. I would develop and present a devestating argument against one person's theology, only to have someone (or sometimes even the same commenter) claim "That's nice, but that argument doesn't apply to my theology." Once I turned against that person's theology, another commenter would make the same protest, all the while my arm grew tired from the labor of whacking off heads. Meanwhile, the immortal head of Liberal Christianity smirks, knowing that it is so malleable that any attempt to pin it down would be like trying to nail Jell-O to the wall. So, for the sake of understanding one another better, I would like to ask two questions of everyone who wishes to join the discussions here.

My first question is to all posters, theist and atheist. According to you, what is the nature of deity? In other words, what are the characteristics absolutely required for something to be called a god, so that if I convinced you that a rock had these features, you would state "This rock is a god." This question is especially important for the atheist/agnostics to answer; how can we call upon the theists to provide evidence that god(s) exist if they don't know what we mean by god?

My second question is, of necessity, directed only at theists. Very few people here claim to know the full nature of God, but almost all of them claim to know something about God. So, I would like to know from every theist who wishes to join the discussion, what do you consider to be the defining characteristics of the god you pray to? What are the characteristics which, if even ONE OF THEM were missing, would cause you to no longer worship that god? This question is fundamental to the argument for theists, just as the first question is fundamental for atheists; how can you expect us to convince you that the existence of your god is improbable if you won't tell us what your god is?

I hope our commenters here will seriously consider these questions and answer them. While I don't think in most cases that this question will allow for the debate to be settled, it will at least help ensure that we are speaking the same language.