I don't see why not. Being agnostic means that you acknowledge that you cannot know whether or not a god or gods exist. Being atheist means that you do not believe that god or gods exist. The two are not mutually exclusive, and most atheists are agnostic atheists. In other words, these individuals do not believe that any gods exist, but acknowledge that they cannot know for certain. Likewise, an agnostic theist would then believe that at least one god exists, but acknowledge that they cannot know for certain.

It makes perfect sense to me.

I think it depends on how you define "God." I do not think that one can be agnostic and believe in the "Christian" God, or Allah, or Jehovah... or even the New Age God. But if you define the idea of God more "generally," then maybe.

Yes. Check out the diagram in this link: [godlessmom.com]

Sure! Technically speaking, everyone is an agnostic as no one can know for sure that there either is, or isn't, some sort of god being in the universe, outside our universe, or that is the universe. People may claim to know--but neither belief nor the lack of it is knowledge. However, I do think one can know that specific gods cannot exist.

Maybe this chart helps explain it:

Why not? Every theist is an atheist theist; they believe in one god and not all the others.