How does a minimum difficulty of 512 make a pool not "fair"?
Because I would submit more shares on lower difficulty. Or am I wrong on this?
Every single pool that uses difficulties greater than 1 (AKA: all of them) multiplies your share submissions by your difficulty. So yes, you'll submit 4 times more work at 128 diff, but it would be the same payment as somebody submitting a single piece of work at 512. Minimum difficulty has zero effect on your payout over any reasonable period of time.
Thanks for the clarification.
However, on the pool that I would like to have, the share is being used to get the proportional BTC reward for the miners. So I hope all miners will approximately get the same payout for the same mining period, regardless of their hashrates. The different will be that the miners who mine in longer time will get more payout than the ones who mine in shorter period. Has this kind of method been used so far? More importantly, does that make sense?