Where exactly does NYX fit into Laura's background? The official timeline seems to indicate that it follows Target X, but that series indicates that Laura returns to the Xavier school immediately after she's released by Rogers. NYX clearly hasn't been Ret Goned out, since its events and characters are referenced in later series such as X-Force and X-23's self-titled solo series.
The best fit would seem to be that the framing story of Rogers and Murdock interrogating Laura takes place after NYX, while the flashbacks to Laura's time with her mother's family takes place in between. After leaving Megan and Debbie, Laura would then make her way to New York where she fell under Zebra Daddy's control (at a time where she's arguably at her most emotionally vulnerable and less likely to fight back). The events of NYX would then push her into tracking down Logan to confront him, leading to her capture by S.H.I.E.L.D. However even this seems to be a bit difficult to reconcile with the narrative of Target X.
How did she fall under Zebra Daddy's control, anyway? He didn't seem to know about her claws (I guess he assumed she used knives for cutting her clients?) so however he got to her, Laura certainly didn't put up much of a fight. Did leaving Megan and Debbie, severing ties with the last of her family, send her into that deep of a depression?
No, killing her mother would have done that. As Laura herself points out, when she was first in New York (this would be before meeting Megan and Debbie) she had such low self esteem that she wound up turning tricks.
The timeline of Target: X' indicates that Megan and Debbie was Laura's first destination after escaping the Facility (she was in California roughly a year after escaping the Facility. She didn't arrive in New York until two years later, per the ending of Innocence Lost, by which time she is shown dressing in a gothic style. This is something she seems to have first picked up from Megan). I think she even outright states in the books she headed there first.
A little reading suggests a certain Fridge Brilliance at work here. First is her immediately going for Megan's really done up clothing (the cover shows how pleased she is with them) and her insistence that she is not hot. Blatant Lies aside her getting into that line of work might be a way of being able to feel hot, but also if not working as a prostitute then certainly the clothing is a way for Laura to regain some control of her life. It's the same as someone abused getting lots of tattoos, or Took a Level in Badass, the clothing at the very least is her way of gaining some form of control.
Answering all three of your points, we get a bit more of a definitive answer in Logan's Legacy; Laura turned to prostitution to survive. Though the timeline is still a bit of a muddled mess (largely because of Claremont's work in Uncanny, which is the hardest part to reconcile) it seems pretty clear that this occurred after leaving Megan and Debbie. She also viewed her body as a foreign thing. We also know from Wolverine's comments in X-Force that Laura at the time likely had no concept of informed consent — he outright tells Cyclops he thinks Laura viewed his invitation to join X-Force as a command. So we likely have a combination of factors involved: Laura was in desperate straits after leaving Megan and Debbie. She didn't recognize she had value as a person and, largely due to her conditioning by the Facility, didn't view her body as a part of her. Zebra Daddy was a figure of authority, and Laura is conditioned to submit to authority, to the point she struggles making her own choices (remember after being removed from X-Force she was begging Logan to give her an order to follow). There's nothing to indicate a desire to gain control of her life at this point, nor any indication her moral compass or a desire to help others played any factor in it.
Guess we can pass this off as Depending on the Writer. Evolution and Target X gave her a clear goal, and plan. When hanging out with Megan we see museums and pet stores are not her thing, but movies and jewelery certainly are. Kind of hard to reconcile that the same woman who took out all the X Men, destroyed Hydra, and had shown to be able to think and act for herself before would see prostitution as a means of survival...unless it was a cause of self harm.
Well, the X-23 in Evolution is a different character entirely. Or at least, a different universe's version of the character. And it could be interpreted that she was beginning to heal in Target: X, but having to give that up to protect Megan undid any such progress she was making.
Then there is the fact Laura has a strong moral code. Maybe she'd be happy eating spicy food and buying diamonds for rest of her life. It's very much shown she's not happy being a killer, or just a killing machine. Thieving the money would be out. Until she found out Zebra Daddy's business ran to pedophilia she was probably okay with what she did, not happy perhaps but certainly much better than she was.
Third, with very few exceptions she finds it hard to say no to those in need. In just a short timeline she ignores Gambit brushing off her concerns and gets him to a doctor, babysits the Richards kids and entertains them (it was them wanting to use a nuke to travel through time she drew the line at) and joins the new Avengers, was it? Stealing the principal's car, going to museums or pet stores may not have been something that held her interest but she did for Megan's sake. Maybe the idea of prostitution was sold to her by helping others. Maybe she had sympathy for her clients.
The problem with this is that Laura doesn't express a desire of her own to help other people until she joins Avengers Academy. During her time with the New X-Men and X-Force she was following orders because she doesn't know how to do anything else (Wolverine states this explicitly in his rant to Cyclops about involving her in X-Force; she only said yes because she doesn't understand she can say no). So I doubt her turning to prostitution had anything to do with sympathy and altruism. Certainly not from the Laura we see introduced in NYX.
Afraid I'm going to have to file Nyx under Fan Discontinuity. I take their word Laura was involved in that but it's too much of a radical change to anything previously established (Evolution) or happened before (Target X.)
As noted above, X-23 in Evolution is an entirely different character. Those events aren't part of the 616 Marvel Universe in which NYX is set. It would be no different than questioning continuity between 616 Wolverine and Ultimate Wolverine. NYX is the first appearance of X-23 in the Earth-615 universe. Evolution is Earth-11052. Two different universes, two different Lauras.
How exactly do Laura's foot claws work? She's shown being able to extend them while her feet are flat on the ground, which would suggest they're actually stored within the foot itself. However not only are they often depicted as being too long for that, but storing the claws in her foot would seem to interfere with the ability of her foot to flex normally when walking.
Conceivably they' be the length of a metatarsal (the the longer bones that form the arch of the foot) and stored between them, allowing them to deploy between the toe knuckles. The length is probably a case of Artistic License – Biology
It's pretty evident that she didn't like the sex worker gig, and goes from threatening men hitting on her to violently ending pimping. Why then does she find gothic fetish wear and black leather appealing. Fanservice aside, she specifically picks out such clothing rather than a more normal look or a more practical outfit. What's up with that?
Laura picked up the look from Megan. Note she raided her cousin's closet for clean clothes upon introducing herself to Debbie in Target: X. Either Laura decided that was how someone her age ought to dress because it's what Megan did (she didn't exactly pick up any fashion pointers from the Facility, so monkey see, monkey do), or possibly she continued doing it afterwards in memory of Megan, who was her first and for a long time only friend. Regardless, her personal sense of style began in Megan's wardrobe.