To start with, nodes no longer mine in Bitcoin. Bitcoin's difficulty is too high, and mining is now done via a series of mining pools, which distribute the work to tens of thousands (if not hundreds of thousands) of ASIC miners.
Mine right away.
Miners do start mining a new block as soon as the previous one is discovered, regardless of if it was discovered by them or another miner.
There is no penalty for mining multiple blocks in a row, since mining is not a operator-linked operation - That is to say, as far as the blockchain is concerned, there is no such thing as defined mining entities, and there is no database or registration against which the blockchain can check to see if a two blocks have been mined by the same entity.
Of course, the output in the coinbase transaction could be checked, but it is trivial to just send that to a new address each time.
Moreover, mining pools would usually assign a different block template to each participant, since ASICs can cover the nonce and timestamp space in a trivial amount of time. They then move on to updating the extraNonce, and by distributing different templates to each miner, pools can ensure work is not done twice.
