Lycanthropy and BAB, Saves, et al.
The lycanthropy template does not change anything it doesn’t say that it changes. That includes BAB and Saves, as well as the size of your hit dice, your various feats and class features, and so on. You can turn into a creature that looks like a wolf, and shares some traits with wolves as stated in the template, but you are not actually turning into a wolf in the sense of replacing your character sheet with that of a wolf.
Aspect of the Beast and different forms
Aspect of the Beast is clearly designed for people who can shapeshift, seeing as it requires that you be able to do so. At no point does it say that its effects apply only to your normal form: it just says that you gain these benefits. Therefore, I’m pretty sure it applies no matter what form you are in.
Change Form: Transmutation (Polymorph)?
Change Form is a polymorph effect, and therefore prevents you from gaining the movement modes and natural weapons of your regular form while in hybrid or animal form. This nixes Aspect of the Beast’s claws. The other options for Aspect of the Beast, however, do function normally: polymorph effects block class features that have to do with your form, but not feats.
Personally, I’d probably allow the claws in both hybrid and animal form, too, because I don’t like taking away characters’ feats. Even with Pathfinder’s slightly more generous feat distribution, I tend to find characters – particularly low-level characters – don’t get enough feats. I wouldn’t want to take any away.