If I have a rig (or more accurately a massive mining farm that is a majority of the hashing power) I have incurred a cost and I am taking a risk by executing an attack. The difference with PoS is that an attack can be executed without cost or risk. That would only be true for PoW if I could build a farm, then sell it, and then somehow execute an attack after the sale with the farm I don't have. It was tongue in cheek to show that since PoW can't be exploited by history, I can't perform an attack with no cost of risk
No, you do not. Because you are anonymous and you can do it over and over again because nobody can punish you for publishing these blocks.
With PoW, it costs energy to do all those hashes, and you also incur the opportunity cost of not using your resources to do honest mining.