Derek Jeter, Mariano Rivera, Jorge Posada and Andy Pettitte, all have won 5 World Series rings.
The player that won the most World Series rings is Yogi Berra with 10. Joe DiMaggio won 9 and Bill Dickey, Phil Rizzuto, Frank Crosetti, and Lou Gehrig won 8 each. Click on the 'Players with the Most Rings' link below to see the list of players that have been on the most World Series winning teams.
Derek Jeter had four World Series rings by 2002.
There are no current players on the Yankees with 7 rings. There are four players with 5 rings (Derek Jeter, Mariano Rivera, Jorge Posada and Andy Pettitte)
Many. See this link for details http://www.baseball-reference.com/leaders/leaders_most_rings.shtml
Andy Pettitte has 5 World Series rings (1996, 1998, 1999, 2000, 2009).