Path of the Beast, Form of the Beast question:

Form of the Beast
3rd-level Path of the Beast feature
When you enter your rage, you can transform, revealing the bestial power within you. Until the rage ends, you manifest a natural weapon. It counts as a simple melee weapon for you, and you add your Strength modifier to the attack and damage rolls when you attack with it, as normal. You choose the weapon’s form each time you rage:

Disregarding the bite, and tail options:

Does the second part of the Claw ability require the following:
1. Raging
2. Attacking with the claw granted by Form of the Beast? If I already have a claw attack, can that trigger the additional attack? (While not raging.*)

It seems very clear from the text you quoted that the claws only exist while you're raging, because the transformation occurs when you enter your rage.

It also seems very clear that the intent is for all of this to apply to the claws granted by this feature and not to any other random claws you might have.

well, darn