Depends on how many people are currently also anonymizing, how many coins you are mixing, etc. The more people there are using it the faster it is. Could take couple of hours, or could take a day. The denomination sizes will be changed (larger denom sizes will be removed) so I think it will make the mixing faster.
Fees are random (this changed just recently), and I guess depend on how many coins you are mixing as well. Maybe someone else will know this one for sure. But obviously you're more likely to hit a fee in 8 tries than just 2.
Currently it has to store the transactions after each mixing round. Haven't seen any discussion about this but I think it's because people can close their wallets after mixing some rounds while there are still more rounds to go. If the transactions weren't recorded after each round, you'd have to start all over from the beginning (and also those mixing with you) if you close the wallet before it has gone through all desired rounds. This could be something where more optimization can be done in the future (i.e. mix using 4 masternodes and then record the tx's, and then mix with yet another 4) when the mixing liquidity is there.