Ending the Faith/Nerissa discussion now (SPOILERS)
Faith is alive.
Faith was at The Woodsmans apartment, because she covered for Lily, which is also alive at this time.
While she was there, Nerissa told Georgie about their plans to blackmail Crane, through the pictures Lily took together with Crane, and Georgie told the Crooked Man about it, and was ordered to “deal” with it. Nerissa feels so guilty that she tells Faith, who has returned from the Woodsmans, while Georgie is at the Crooked Mans place. Faith can’t believe her, and they argue, which can be seen in the photo in Chapter 5.
Nerissa understands what she has brought upon them and promptly gets hold of some glamours either via. The money they already saved for when they were supposed to leave, or just by going to Greenleaf, who surely thought it was for business reasons. (don’t say its assuming too much, the same goes the other way around. Georgie wouldn’t be curious that Faith was running around if he killed her, and that Nerissa was smart enough to figure out that, knot knowing the Woodsman would drive him mad, and hit her, therefore making Toad call Bigby, and that Bigby actually had the time to check a drunk lowlifes apartment to see what the ruckus was about. Also she would have to get a glamour to look like Faith, after her body was dumped)
So now we have Faith glamoured as Nerissa, and trying to find a way to save herself before the glamour wears off(how long they last I dunno, and there is no saying how far away a glamour tube can be from the subject. My thoughts are that they just have to be assigned to the person) How she knows where Nerissas head is, I don’t know, but that would be the same if it were Nerissa who was alive.
She gets the head, and puts what she believes to be strong clues with it, to give the doggy a scent to go by. 
When all this is happening, she knows she cant stay in the town, or that she doesn’t want to (works with her fairytale as well I suppose) and lets Lawrence know that she is leaving for good, and that he shouldn’t look for her.
We meet her next in the Puddin’n’Pie where Georgie isn’t too happy with her performance on the pole. Some speculate that this is Nerissa and that her legs hurt, because of her fairytale, but I believe it’s because Faith needs to imitate Nerissas moves which were clearly inspired by the way a mermaid moves. She’s having some trouble with it.
She gives the address to the motel to Bigby so he can continue investigating. He discovers the room which Lily was killed the day before, and also finds the envelope with the pictures of Crane and Lily, which Georgie didn’t know was there, or didn’t care about, since he didn’t expect people to snoop around that room.
Now we have two heads and one body.
Swineheart is having trouble indentifying and examining the Faith head because of the glamour, and Lily’s glamour wears off when her glamour tube is opened.
The list goes on and on, but this is what I believe is substantial evidence to knowing Faith is alive at the end.
Also if it were Nerissa, then why would the sentences that are mentioned in the end even be there.
Im talking about Swineheart having trouble identifying the body, Faith saying “You’re not as bad as everyone thinks you are”, and the rest.
If you have any reasons to believe otherwise, let me know. I wanna see if i can prove my point further.
TL:DR: Faith is alive, we never met Nerissa, and i am ready to solve your puzzles and reasons to believe otherwise.
Comments
Or Nerissa was glamoured as Faith in ep 1 and we never met faith. i do think it being Faith is more likely given her story.
Mmmm, I'm with you with most of it. :-)
But who killed Nerissa and why? How could Nerissa accept to have been glamoured as Faith and the high chance of being killed?
Sorry for the late reply.
Georgie killed Nerissa while she was glamoured as Faith. She accepted this because it was all her fault that Georgie was after the girls in the first place. Her fellow dancers were her last joy in life, in a way, so she decided to switch places before Georgie got to Faith as well. She did it out of love.
Yeah, this doesn't really explain the identical bruising on Faith's head when we save her and faith decapitated head when we find it.