I don't want to get dragged in an argument about what atheism is, but the commonly accepted definition is that it is nothing more or less than the belief that no god exists.
The big bang has exactly nothing to do with atheism (why bring it up at all ? it's just a science topic) and "believing that a god exists but deciding, like an atheist, not to follow any rules" is not being an atheist. It is being a believer in some god (so, a theist) as well as an anarchist.
ALL your examples were people that are very clearly not atheists, since all of these examples involved believing in one god. They are only various examples of monotheist practices.
There can not be branches of atheism - and I know I'm exposing myself to a misguided answer making reference to the no true Scotsman fallacy, but it would be wrong. The very etymology of "atheism" leaves no place to branches: if you believe that a god exists, good, even if you think there is only one this still leaves many ways to believe in it... however, if you believe that no god exists, which is what atheism is, there is only one way for something not to exist at all.
There is a fundamental difference between believing something exists and believing something does not exist. Believing that it does not exist is a very simple belief, with no possible nuances while believing in the existence of something does leave place to interpretation.