Do natural attacks [Catfolk/Tengu claws] count as unarmed attacks for feats like Boar Style?
No, they're not the same.
Unarmed Attacks and Natural Attacks both attack using Natural Weapons (ie. the parts on your body and cannot be disarmed), but that doesn't mean an Unarmed Attack is the same as a Natural Attack.
However, Feral Combat Training (I think that's the feat's name) allows you to apply any feat with an Improved Unarmed Strike requirement towards Natural Attacks.
OK so for Boar style you'd need a two feat investment to get the +2d6 bleed damage.
OK so for Boar style you'd need a two feat investment to get the +2d6 bleed damage.
Technically 3. To apply Boar Style to a natural attack, you'd need Feral Combat Training (which requires Improved Unarmed Strike and Weapon Focus in the Natural Attack you want to use it with) and Improved Unarmed Strike, which you already got through the requirements for Feral Combat Training.
If you're doing this with a Monk, you thankfully get Improved Unarmed Strike as a bonus feat.
And the unarmed fighter!