Suppose I am about to hit a "overhead", then my stomach touches the edge of the table... Is this allowed? Can I "dive" on the table?
No you are not allowed your stomach to touch the table espically when serving. Your free hand is allowed to touch the table but through out the play you are not allowed to touch the table with any body part. But you can lean on the table if you are trying to hit the table tennis ball in play but not when you are serving. See AU table tennis rules for more information why you are not allowed.
My understanding after reading the rules is: as far as the touch does not move the table it should be O.K. otherwise it's a point to the opponent. The last three (in italic) points govern the "contact":
2.10 A POINT
2.10.01 Unless the rally is a let, a player shall score a point:
2.10.01.01 if an opponent fails to make a correct service;
2.10.01.02 if an opponent fails to make a correct return;
2.10.01.03 if, after he or she has made a service or a return, the ball touches anything other than the net assembly before being struck by an opponent;
2.10.01.04 if the ball passes over his or her court or beyond his or her end line without touching his or her court, after being struck by an opponent;
2.10.01.05 if an opponent obstructs the ball;
2.10.01.06 if an opponent deliberately strikes the ball twice in succession;
2.10.01.07 if an opponent strikes the ball with a side of the racket blade whose surface does not comply with the requirements of 2.4.3, 2.4.4 and 2.4.5;
2.10.01.08 if an opponent, or anything an opponent wears or carries, moves the playing surface;
2.10.01.09 if an opponent, or anything an opponent wears or carries, touches the net assembly;
2.10.01.10 if an opponent's free hand touches the playing surface;