What happens then? Well, @anyx's node knows exactly which node is posting the next block.

No. A randomnly selected non-consensus witness signs a block every 1/21 times.

Rather than having to share that information with the entire network, he simply has to send it to the single node that's scheduled to produce the next block. This makes everything much more efficient, especially if it was @anyx's node that was going to post the next block.

On a blockchain, all transactions are public. You cannot not share on chain transactions with all witness nodes without breaking the chain.

Every atomic swap needs four transactions, two on both chains. The real efficiency gain is that Hive uses DPoS and not PoW. Calculating a few hashes for the purposes of the time-locked contract is not too much work.