Should Facebook and Facebooking be capitalized?

Yes, it should. As you can see from the 'Terms' on the Facebook site, 'Facebook' is always capitalized.

The logo has nothing to do with if it should be capitalized or not. Facebook is a proper noun, therefore you capitalize it. It's odd that people would think otherwise, because you wouldn't put something in all caps just because the logo is in all caps, would you?