Can I use the claws with iterative attacks from high BAB? How do two claws interact with TWF?
Natural attacks do not get iteratives, and if you are exclusively attacking with natural weapons then TWF does not apply.
You can only use one claw attack as a standard action, but can make all your natural attacks as a full round action.
Basically I'm grooving on the idea of the shadowy demon ninja that kills with his bare claws, I'm just not 100% up on what all would be required for a good mauling.
Usually aiming for three natural attacks is a good idea. A Tengu for example can get three natural attacks out of the gate. If you wanted a way to add a third to a tiefling ninja might I recommend Skill focus and eldritch heritage for the sorcerer's Serpentine bloodline.
Additionaly, I know I can enhance base claw damage with Improved Natural Weapons monstrous feat, but I assume that just like a monk the only way I could enchant my claws is with the amulet of mighty fists?
Typically one would use an amulet of mighty fists, but it's not the only way. Getting someone to cast Magic Fang for example, or acquiring an oil of it. There is also the Body Wrap of Mighty Strikes. There may be other examples as well, however the Amulet is likely your best bet for long term investment.
There has been a lot of discussion of mixing natural attacks with unarmed strikes and i would like to clarify how this would work
Let us take a level 8 ninja, weapon finesse, 18 dex, with a +1 agile amulet of mighty fists. Your attack bonus would be at +11 with everything mentioned.
If you just do a full attack of natural attacks of Claw/Claw/Bite
Each one would taken at your full bonus of +11 with a damage bonus of +5 (and Sneak Attack if applicable).
Lets say you wanted to throw in Unarmed Strikes (as kicks or whatever) here is how that would look -
Unarmed Strike +11/+6
Damage bonus +5
Claw/Claw/Bite all at +6
Damage bonus +3