theories on the crimes
there have been two decapitations, two cases of breaking and entering, two beatings and one case (i suspect) of some kind of coercion to suicide.
i suspect one of the beatings (the one given to Faith by the huntsman) is not connected to the bigger case, i believe the huntsman hired faith for her..services and he only beat her because she didn't know who he was.
the other beating was committed by Dee/Dum on toad to find something he suspected Faith left in the building
the two breaking and enterings committed by Dee and Dum were to find Faith or more information about her.
the two decapitations were committed by an unknown person/s for an unknown reason.
the (suspected) coercion to suicide seems to have a magical element to it that made Lawrence think he was dreaming, maybe the person who did this used some kind of magical interrogation technique to get information and convinced him to commit suicide so he would never remember what happened.
i believe there are two groups (or possibly more) of criminals looking for the same unknown thing, i think Dee and Dum are working for a criminal who wants the same thing the murderer wants, but i don't think they are working together, so Dee/Dum didn't commit the murders.
clearly the murderer wants to send a message but who is the message for?
maybe its for Beauty (what is she sneaking out for?) maybe its for Crane, or maybe it's for Bigby, who knows?
whatever the motives i think there are two (or more) groups of people looking for the same thing/person, and this thing/person must be very powerful for them to be willing to kill fables and maybe alert the Mundies.
if anybody else has more theories put them here.
My theory is Dee and Dumb are Bluebeard's henchmen, Lawrence owed Bluebeard a large sum of money having no way to get out of it Faith took to the streets to earn the funds to pay back Bluebeard, but they're not the killers. The Tweedles operate during the day while the killer hunts his prey at night. Also they don't seem the sort to have a lot of grace or tact ( Dee getting caught twice by Bigby). Also it seems the suspect is targeting Royalty, namely princesses ( Snow and Faith). Could the killer be of royal blood back in their fairytale land? If so, would that cause the killer to become jealous and resentful towards the other princesses?
Also I would like to point out that it's a class issue as far as only the wealthy Fables get treated properly while everyone else twists in the wind because Faith not living in the best conditions ( dead beat boyfriend, is a working girl). If it was a message about how the rest of the Fables were treated wouldn't you think the killer would target the better off Fables in the Bronx rather than a working girl trying to get out of debt from a loanshark?
yeah, this does seem to be a story about class, and i think you are right that Dee/Dum are working for blue beard, he seems to be someone who would hire henchmen