A question about defining 'Atheist'

[Dystopia]

1. I've heard some say it's not that the atheist has a belief in no-god, but rather a rejection of the proposition that God exists. How are these two positions different?

It's really a distinction that doesn't bother me. I'd say an atheist can simply lack belief in any gods (maybe that's what you meant in the first part of question 1 'belief in no-god') or disbelieve the existence of gods. I can be wrong but I think actively not believing in gods (taking as a proposition 'god doesn't exist) is the same as rejecting the proposition that god exists. If I don't believe, I reject the proposition

2. If an atheist accepts that there is a difference between rejecting the belief in the existence of deities and asserting they do not exist (asserting the former not the latter), does that differ from the assertion that God does exist, but he/she rejects belief in God?

I think both are more or less similar, it's a conceptual problem. It's just as valid as theists accepting belief in god and god not existing

3. If you assume the reliability of the law of the excluded middle, then logically speaking there are only two possibilities: God exists or God does not exist. By definition, there cannot be 'maybe God exists.' (I want to clarify here that I'm not proposing a person can't be in a process of inquiry where they are testing the truth of one or both of these propositions and so are 'wondering if God exists', but rather there is no logical conclusion that 'maybe God exists') Given only two possibilities, is assigning a truth value to the proposition 'God exists' of false, does that necessitate assigning a 'true' truth values to the proposition 'God does not exist'? In other words, if you reject the propostion 'God exists' does that necessitate you conclude the proposition 'God does not exist'?

Yes, from a belief perspective/proposition, not from a knowledge proposition

4. Also involving the law of excluded middle, is the position of 'agnostic' (maybe there is a God) logically sound?

Agnosticism is a knowledge proposition, an agnostic doesn't think 'maybe there is a god', an agnostic claims to not know if a god exists. An agnostic can be an atheist or a theist, in my case I'm in an agnostic atheist, I lack belief in any gods but I don't claim to know if they exist or not with absolute certainty

5. Does the law of excluded middle allow for a neutral position (maybe God exists) with which to begin logical inquiry?

The only option that is close to your proposal is agnostic theism, but I don't think it's possible to believe maybe god exists, either you believe or you don't

6. It seems that the rejection of the proposition 'God exists' is a postion the atheist takes. If you reject the proposition that 'God exists' are you required to defend this position?

If someone accuses me of a crime, that person is the one who needs to prove I practiced it. The one who makes a positive claim has the burden of proof

7. If I as a theist were to reject the proposition that 'there is no-god', would I have to defend this position?

No, but you could make your arguments for losing faith, nothing wrong with that, it's advisable

8. Atheism is to Biblical Christianity as agnosticism is to deism. Is this an accurate relation of terms?

No, this doesn't make any sense... Why are you even relating knowledge with personal belief? I can be an agnostic while being an atheist, deist or theist

9. What label would you prefer to describe your worldview/religion? Please provide a definition and/or brief explanation.

Agnostic atheist, but I don't promise in the future I won't sweep to gnostic atheism. Regarding religions I sometimes sweep to gnostic atheism, I can use the evidence such as contradiction in holy books or contradictory characteristics in gods to prove religions are unreliable. As for simple theism or deism without any specific religion I can't prove a god doesn't exist, therefore I am an agnostic atheist