That seems reasonably accurate. But which god, exactly? There are so many.
The great thing about statements of the form that some person "doesn't believe in X" is that, for any term X (e.g., "god"), there exists no entity, thing, process, etc., that is X and that this person believes in. Even less formally, to not believe god exist simply requires that I believe nothing exists which I would say is god, and anything that I would say is god or a god is something I don't believe exists.
There are lots of descriptions of elves in various languages. To assert elves don't exist, you need not know of the Teleri or Noldor.
You lost me there. Why must you insist that just because a person is unconvinced regarding a proposition that they must therefore ascribe to it's opposite?
I don't. If one doesn't believe god exists but it is not true of this person to say that they believe god doesn't exist, they are not atheists (they are most likely agnostic).
I'm not positively convinced regarding the existence of the Loch Ness Monster, but that doesn't mean I positively believe that it doesn't exist.
You can remain unconvinced about the ontological status of god, the Loch Ness monster, big foot, etc., and yet believe that none of these exists as opposed to the agnostic position in which you assert merely that you don't know (you can make this more formal with belief functions or subjective probabilities, but the essence remains: if there exists enough evidence for you to conclude that you can say more that "I don't know", even if you don't actually know the truth based upon the evidence you need only evaluate it as sufficient to warrant a verdict; in this sense we might compare belief to a verdict or, as is done often in epistemology, the philosophy of probability, etc., to bets- juries don't actually know guilty parties but are asked to render a verdict in criminal trials based on whether the evidence is reasonably sufficient to "prove" guilt, while a rational gambler will not place a bet on the truth of the statement for which she has little cause to think is either true or false).
Although it seems like a laughably remote possibility, it might exist.
Almost the entire point of mental state predicates like "believe", and epistemic modality more generally, is to enable claims/assertions about what "is" or what is "true" without requiring that such statements be correct. Thus I can say that "I believe that whatever doesn't kill you simply makes you stranger" if in fact this is a position I support or regard as truth even though I can simultaneously state (truthfully) that I don't "know for a fact" that my position is true.
Isn't that because Agnosticism is essentially a shrug regarding the proposition that one can know that god exists?
Any proposition of the form "x knows y" isn't actually a proposition in logic (or rather, requires "deviant" logics for admission). Mental state predicates in general are not admitted as propositions. However, the pragmatic basis for the continued term that Huxley coined is not so much a certainty as to whether or not a statement about knowledge of god is impossible, but a subjective epistemological claim (namely, that one doesn't know whether god beliefs, or better yet one does not know enough given the evidence such that one would place wagers according to formal probabilities or game-theoretic systems involving rational payoffs).
Or are they merely asked to believe?
Belief that god exists isn't the same as knowing god exists, but because any belief claim is a claim to have knowledge we demarcate those whose belief claim is that god exists from those whose belief claim is that no god exists, and both from the position that one can only say they don't believe god exists, not that they believe god doesn't.