Empirically, it seems to work so far. My likes are quite eclectic, too, but that's by my design -- my homepage gets feeds related to Machete Kills and Oscar Wilde because I actually like both. Most of the ads are obviously wrong (hair conditioning products and club wear; I'm bald and hate clubs).
I honestly don't care about targeted advertising. Irrelevant advertising works fine for me.
Nah, you just get adverts you care even less about than those which have a chance of being some measurable fraction of relevant.
Most of the adverts I see seem to be based on what my contacts have "like"d, or otherwise interacted with, more than what I have done (though this could be in part due to me providing fb with a lot less info to work on than some of my contacts do) so providing fake information about yourself will make little difference there unless your contacts all do the same.