The correct word would be "antitheist"

I guess you can hate god as a concept. God can be proven to exists in human minds (no esoteric stuff, just psychology and sociology). You can hate this scientific fact and what it means for humankind.

Tbf, you can think god isn't "real" while also hating the concept of "god" for being responsible for so much war and division throughout history (among other reasons.)

People hate on fictional characters all the time though.

There is a difference between god as a character and God as a concept; the former one is (in my belief) nonexistent, the latter exists as long as his worshipper worship him.

I dunno. I'm not entirely an atheist (my religion is blasphemy. If the gods exist, they like a target) but I can hate something I don't think exists. Some of those deities are godsdamned genocidal maniacs and pedophiles.

Since we are already being unhelpful: Atheist don't all are unsure about if God exists. Some may believe God does not exist, some don't care. Some believers might be unsure or don't care either.