Can a miner remain anonymous? 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.
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:


http://www.blockchain.info/connected-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.