Jack and crew interactions? You should probably call it Jack vs. The Crew

Jack and Grunt couldn't not get on, really... they both were 'made' what they are, they both admire Shepard in their own ways, and they both have a 'take no **** and take no prisoners' attitude. They like a good fight. And while they'd probably disagree over the semantics of various issues, it'd probably go no further than a
"Yeah, whatever," and it's on to the next one.
While she could appreciate Thane's skill, I doubt she'd respond to his spirituality with anything other than cynicism, perhaps suggesting that he uses it as an excuse or an emotional crutch for his actions. Jack's a realist; if she can't see it, hear it or steal it, it's not really worthwhile. And if you had her experiences with a cult, or hell, her childhood, would you buy any kind of spirituality? If any kind of God showed up to you, you'd knock their teeth out before you took a knee.
Jack and Miri... oh, I don't see that ever working. Even if Miranda got off her high horse, Jack wouldn't get off hers. I don't even think Jack would accept an apology from her; it'd be too much like giving in, or it'd be too great a risk of opening herself to exploitation again. Even if Miranda went on a demolitions spree at Cerberus bases, it'd never be enough. Some things don't heal. Ever.
I think almost everyone else on board ship would be ignored. She might exchange words if she feels like it with Zaeed (because of his career choices) or Tali or Garrus (because they've known Shepard for longer) but outside of those conversations on her own terms, Jack seems likely to just walk by people. No acknowledgements, no thank-yous, no pleases. If she wants something, she helps herself to it, and once she has it, it's hers; she goes up to the women's washroom and another woman walks in, they at best will get bawled out, at worst will end up sat outside with a broken nose. You bump into her, you get bounced off a wall. And if you open your mouth... chances are the Varren is coming off the leash.
On the other side of the coin though, places with a lot of people, like the mess hall, would be one of the few things that would scare her. People with experience of prison messes don't react well to sharing personal space (hell, prison period does that to people). Someone offers her something out of simple politeness will find themselves eating it, someone staring at her a second too long will find tabletop added to their diet. As soon as it's done though, Jack would know it was an incorrect reaction; a stain from prison life making itself known on autopilot. So, she would avoid any confrontations; slope up at the end of the day and eat whatever was leftover, taking a tray back downstairs with her or only sitting in the mess when absolutely no-one was around, or eating only when Grunt was there (as he's bound to clear the mess... regular folk don't find Krogan relaxing company) or if Shep dragged her ass in there (and even then she'd act up and **** until the endurance test was over). There's probably a small mountain of trays slung behind all those pipes below engineering. After a few months down there it would probably be more of a mess than your average collegeboy's pad.
Oddly enough though, I think Samara would be the one person on the ship besides Shepard that would understand Jack. She may be bound be her Code, but she could certainly appreciate what has made Jack into the woman she is. She'd probably feel deeply sad for her, seeing someone too damaged to function any other way, too weak to have made any other choices that stand on the higher moral path. Samara would almost certainly see though that Jack and the Normandy (or Jack and Shepard if the Shep is male and pursuing her) is something close to therapy; a chance to finally be someone outside of the shadows of the past. She would watch closely, but I doubt she would intervene without giving Shepard some prior warning. Besides, it would be all too easy for her to react in similar ways to Thane or Zaeed, who have also made lives for themselves outside of the natural realm of law and order. Samara on the Normandy has to know when to ease off, unless something's done in front of her I'd suppose.
Just my take, 'tis all :happy: