Who decided what the existing minimum fees are? Greenspan?
No-one, since there is no such thing currently. You can push transactions out with whatever fee you wish, including 0. Wallets will usually recommend a fee though, how that fee is decided is presumably decided by the developers of the wallet in question. Miners, in turn, choose what fees, if any, they require for their services. You might say it's a fee market.
Correct - but you are relying on the kindness of strangers to get your tx in to a block. and that will only happen if there is spare capacity ( i.e it costs the miner zero to include it ) But bear in mind that the old 'reserved' portion of the block (50K) for free priority tx's is now gone (by default) and that the concept of priority is about to be killed off entirely, I think its fair to say that the idea of free tx's is dead.