by the nodes with enforcing the standard rules that would be rejecting any transaction that is non-standard or has large OP_RETURN data (which is what you would use to push arbitrary data to the blockchain). and that is enforced per transaction basis since there is no other way.

again, bitcoin blockchain is not for data storage. use an altcoin that is designed for that. there are actually a couple of them: SIA, storej, filecoin,...