Ask to meet this dude's parents. It's an unorthodox but surprisingly simple and effective way to tell us if this guy's secretly a bandit or something. On an unrelated note, it's good to know that Veila can learn magic just by watching us - she'll get to learn magic without affecting our own studies.
Considering his clothing, and the fact he seems to have spent several days at this tavern you do not think he is a local. Part of his introduction also included the implication that he is accustomed to travel, but that he has never been far outside Arfelt, the Kingdom you are currently within.
That she can! Many skills give careful observers experience, but only on successful checks, and that's dependant on the skill level of the person being observed. That means that for the moment, Veila has gained experience from watching you do magic, but very little. Your failed attempt to teach her was not a waste of time either, as it gave her the opportunity to roll to learn a cantrip, and gave you a little more experience. She failed, but the attempt still gave her experience, if you had succeeded on your check you would have given her a bonus to her own roll. As is she can only gain experience in magic from observing you successfully perform magic, or by having you teach her, as she lacks the necessary materials or baseline of experience to practice on her own.
These mechanics also mean that your companions have been gaining a little woodcraft experience from your own routine checks, and that the whole party gained bargaining experience from observing the more experienced Kellay bargain on your behalf around town.
I've already used the word experience too much, i will have to overuse some other synonyms in the future.