Can I add non-contact fields (such as membership, contribution, relationship, etc) in bulk emails?
The short answer is "not without extensions". It would be difficult, for instance, to say exactly which of a contact's many contributions you want to pull data from.

That said, other users have created extensions that give you many of the most commonly needed tokens. Check out the Summary Fields, Contributions Table, and Eileen's custom tokens, in that order.