Can you differentiate the miners from the normal clients, by doing some frequency analysis on ip-addresses that announce new blocks? Or will the new block propagate so fast around the network by normal clients that it's impossible.
It is trivial for solo miners to use tor to hide IP adresses. This defeats mentioned above frequency analysis attack.
I don't know what this frequency analysis technique would do, so this answer corresponds to the second question you asked:
Blockchain.info connects to hundreds of nodes:
The IP address Blockchain.info shows is the address of one of those nodes that they happened to be connected to which first saw that transaction. A node where privacy is desired does not allow incoming connections and only connects to trusted nodes that won't violate privacy expectations.