Who pays me when pool mining? When I pool mine, do my payments come from the pool operator's personal account? From the pool's wallet? Or from somewhere else?

When using P2Pool, the payments appear in bitcoin-qt as though I had mined the block myself.
Broadly speaking, there are two ways of paying pool miners. The first way is to have a wallet and send payments to miners through that when they ask for them.

The second way, which both eligius.st and p2pool use, is to keep track of how many shares people get, and set the coinbase transaction to pay the block reward directly to them once a block is found. This has the advantage that you never have any Bitcoins to steal on your pool server.