More than a synthesis, it is actually not a religion in a strict sense, rather a collection of philosophies and ideas. Hence its extremely large variety in form, and also its self-contradictory nature (this isn't a feature of Hinduism alone, but of most other faiths). And the brunt of these ideas pre-date the South-West Asian monotheism.
You're right. Hinduism is more of a conglomeration. I suspect that some of its roots go even further back that any of us can imagine.
Whenever someone asks about the creation story of Hinduism, the best answer is: Which one?
More like classical polytheism. The difference is, so far as I know anyway, is that there are no gods associated with city-states.