Are there any diplomatic consequences for agreeing to unfavorable (to me) trade agreements?

Looks like this was updated in the June 2011 patch:

[A diplomatic change] Track trades between players and allow that to positively influence relationships (the better the deal for the AI, the stronger the modifier). Particularly useful for bribing a hostile AI.

So it seems these sort of trade agreements do indeed have impact, at least since the patch.

In my experience, yes, eventually. There seem to be bonuses like "Our trade relations have been fair and forthright" or somesuch. In practice I've always found this bonus rather hard to obtain however, and don't forget that dealing with one civ will often upset another civ - and that effect is much stronger. Watch out!