Is it possible to have BIND transfer all the second level domains for a single TLD to my local machine? (I'm fully aware that this would be a massive data set)
Also, how do I track changes on a daily basis?
Theoretically maybe, but in reality almost every properly configures their domain servers to not permit zone transfers to un-trusted sources (in this case you).
So in the practical reality, the answer is no this is not possible.