Transforming Pet's Skills

I just purchased a Bombay not long ago. I know they are compatible with the Dark Knight transformation, but.

When I transform, will the Bombay have the same exact skills and exact ranks as mine? Like, if I had Rank 3 Body of Chaos, the cat will have Rank 3 Body of Chaos too?

Yes, that's what makes them so useful, they gain EVERY boost that you get, I don't know if the 60-100-180 applies to them, but as far as I know, the only thing they don't get is Control of Darkness.