Can the benefits of Melee Weapon Mastery apply also to a natural attack? For example, a bite is listed as bludgeoning, piercing, and slashing. If someone has MWM of any flavor, can those bonuses also apply to a secondary bite attack?
Since a bite attack is an attack with a weapon that deals the selected type of damage, the bonus applies.
If your DM is picky, it's conceivable that he's only apply the bonus to the strikes which use that damage type - i.e. vs. a creature with DR/bludgeoning, only melee weapon mastery bludgeoning would apply. That's still within the concept of the feat, although the plain rules text doesn't dictate this limitation (and I wouldn't bother as a DM).
I don't think so. I don't believe that a 'natural attack' is a 'melee weapon' per se, and so wouldn't qualify. But it's late over here, so I could be wrong.