As far as I can tell nothing prevents this in theory however Blood Drinker is not a PFS legal feat according to the Archives of Nethys website which is considered an official rules source I believe for PFS. Even if it was legal the feat itself states that feeding off an unwilling intelligent creature is an evil act. Repeated use of this feat would likely cause an alignment shift towards evil and eventually require costly atonement spells or the loss of the ability to play the character as you may not play an evil character in PFS to my knowledge.
You’re welcome :)
Normally, you can only drink blood from an opponent who is helpless, grappled, paralyzed, pinned, unconscious, or similarly disabled. If you have a bite attack, you can drink blood automatically as part of your bite attack; otherwise, you must first cut your target by dealing 1 hit point of damage with a slashing or piercing weapon (though you may feed upon a creature with severe wounds or a bleed effect without cutting it first). Once you cut the target, you can drink from its wound as a standard action. Drinking blood deals 2 points of Constitution damage to the creature you feed upon.
Drinking is a standard action so you cannot drink twice from a target that is cut.
On occasion, a dhampir may inherit his father’s lengthy canines. Whenever the dhampir makes a grapple combat maneuver check to damage an opponent, he can choose to bite his opponent, dealing 1d3 points of damage as if using a natural bite attack. As a standard action, the dhampir can bite a creature that is bound, helpless, paralyzed, or similarly unable to defend itself. This racial trait replaces the spell-like ability racial trait.
Even if you have the fang alternate racial trait it is still a standard action to bite a helpless target.
So, no you cannot drink twice in a round.
To clarify my earlier statement a little the Fangs alternate racial trait only allows you to make your bite attack as part of a combat maneuver check to maintain a grapple when you choose to deal damage as part of that check so you can’t use them to bite your target on the initial check to initiate the grapple. Yes Greater Grapple and Rapid Grappler allow you to make grapple checks to maintain a grapple as a move action and a swift action respectively. So on the second round of the grapple you may make up to 3 checks (as a standard, a move, and a swift action). On any successful check you may choose to deal damage with your bite attack so you can potentially bite your target up to 3 times starting in the second round of the grapple. As Mysterious Stranger quoted “If you have a bite attack, you can drink blood automatically as part of your bite attack” so drinking blood can be done as part of the action made to bite the target and can be done with each successful bite attack made so in this case up to 3 times potentially.