I'm pretty sure that "sock yarn" just means that it's very lightweight (so it won't be too bulky for inside shoes), doesn't have too big an acrylic content, and is machine washable. These aren't all always true, but I think that's the main difference. Some make cool designs when you knit them, too.
You need to bind it off. To do that, knit the first two stitches in the row. Put your needle through the first stitch you knit, and pull it over the second stitch you knit, off of the needle. If that doesn't make sense (and it might not, because I think that it's hard to learn/relearn knitting just with reading words), check out knittinghelp.com
Raising a stink might result in you missing your plane while they question you about your sinister craft-supply-related plot ... people in authority don't like to have their authority questioned. You push, they are going to push back. I would try polite requests instead of stink-raising.
On top of that, it can get you in longer-lasting trouble than just a missed flight. My parents flew somewhere last fall, and on the way home my mom realized she was missing her license. She had a student ID with her, but since she's not the expected age of a college student, the person at the check-in counter didn't want to let her get on (of course, the ID worked on the out-bound flight, but oh well). She caused a big stink about that, of course. Then a few weeks ago, she came to visit me and brought a bunch of polymer clay/polymer clay accessories. Due to the funny shapes, rubber gloves, and white powder, her bag was searched and some of her stuff was actually taken out - it's at the screener's discretion. Anyway, after that long story, my mom is now pretty sure that she's on some kind of watchlist, whether it's from the argument at the airport, or the weird stuff in her suitcase. So don't cause a stink. Be prepared to self-send your stuff home, or just put it in your checked luggage to begin with.
I'm sure you'd be okay with a crochet hook, since it's not listed as specifically not allowed. But one thing to keep in mind is just that, at least here in the US, sometimes things that are allowed on airplanes aren't - it's at the security guards' discretion. So it is possible that even a crochet hook won't be allowed on.
Honestly, I think your best bet really is to just hold off on the sweater. For one thing, even a wrap sweater gets bulky and unflattering on someone who's 30 pounds too small for it. The torso might wrap around, but the sleeves and shoulders don't. Plus, I know that if someone made me a sweater while I was working to lose a significant amount of weight, I would appreciate it, but I wouldn't be able to really use it. I say you explain to her that you want to make her a sweater, but you're going to wait until she's ready for one. In the meantime, she can pick a pattern/yarn that she likes and (assuming it's doable for you) then you can make it for her. Unless this is going to be a surprise gift, I bet she would appreciate it a lot more, because she helped in creating it. Plus you'll know it's something she's going to want, so it's also something she'll likely use.
Okay, so I realllllllllllllllly want a set. I'd love to not have to buy 20 pairs of needles everytime I make a sweater, and they seem like a really good way to avoid that. I was at the yarn store this past weekend and talked to the wonderful ladies that work there, and they both recommended different sets for different reasons. Since I can't try out every set before I buy, I was hoping that anyone that has a set could let me know what their needles are like, why they like them (or don't), and that kind of thing. Thank you so much!