No. They are mutually exclusive. An atheist does not believe in a god. An agnostic doubts there is a god.
Not quite. Atheism is a position on belief, agnosticism is a position on knowledge.
An atheist does not
believe god exists, while an agnostic does not claim to
know whether or not god exists. Belief in absence, and absence of knowledge, two distinct concepts that are perfectly capable of co-existing.
It's entirely possible to believe that it's not possible to know for certain that your position is correct, while at the same time believing that your position is correct.
Pretty much: I'm very sure I'm right, but there is a hypothetical possibility I'm wrong.
For example, if you find a discarded lotto ticket on the street, you can believe with a high degree of certainty that it isn't the winning ticket without actually having checked the numbers to make sure that is isn't the winning ticket. Sure, you'd admit that you don't
know it isn't the winning ticket, but you can reasonably
believe it isn't
In the case of the agnostic atheist, the ticket would be the universe, a winning ticket would be a universe with God, and checking the numbers would be finding indisputable evidence as to whether or not God exists.