Atheism is an absence of belief, not a belief in absence.
You know that those are logically identical, right?
No they aren't.
A simplified example: "John doesn't believe God exists" is identical to "John believes God does not exist" as they both expresses, unambiguously, John's beliefs about the existence of God. That is, to the question "Does John believe God exists" both statements evaluate the same way: "no".
Wrong question. Ask "Does John believe there is no god?" and in the 2nd instance the answer is "Yes". In the first instance, you aren't provided with enough information to answer the question.
As a general rule, "yes" and "I don't know" aren't equivalent just because neither means "no".