The unarmed strikes are not dependent on specific limbs. As far as the system cares you could be humping them really hard to get your unarmed strikes.

The interaction with the claws is the same of natural attacks: You do all your iterative attacks, then all your natural attacks on top of it. If I recall correctly, the natural attacks are done at -5 that way.

unarmed strike and natural weapons are not treated by the same feats and effects. Superior Unarmed Strike doesn't touch the claws, and Improved Natural Attack doesn't touch the unarmed strikes.