It appears to me that to mine Nasty Mining, one must be a Nasty Fans member. Is that correct?
No. Anyone can mine on NastyPool. You just need to point your miner at nastyfans.org:9332 and use your Bitcoin address as your username to receive payouts.
If a member, and one is mining Nasty Mining, are all mined rewards paid out to the member or are some automatically retained by Nasty Mining and/or NastyFans?
If you are using a Bitcoin address as your username, 100% of mined bitcoins are paid out to you.
Is mining at the Nasty Mining P2P node same as mining at any other P2P node other than the added benefits of the NastyFans relationship?
No. Mining on NastyPool (our p2pool node) will track the number of accepted p2pool shares and display this information on the mining tab of nastyfans.org when you log in and select your address. These accepted p2pool shares will act as lottery tickets for a future incentive program. There are other benefits that are coming down the line, but for now the lotto tickets and p2pool accepted share counter at nastyfans.org are the benefits to using our node.