Will my transaction remain with zero confirmations for the next ten blocks?
I think it would be
at least 10 blocks; your transaction may get stuck in a backlog of free transactions that can't all fit into the next block. Which seems to be happening for real right now...
If this is the case, I don't see why any miners would have any incentive to process no-fee transactions. If they get the new-block 50BTC regardless, they lose nothing by requiring fees and can potentially gain.