Hey Georgia! I'm going to try to answer your questions, but if you have more, feel free to ask more!
1.) I would think that a "magical watch" would simply be a watch having any sort of magical properties that might benefit a wizard? Think of the grandfather clock at the Weasley's. Maybe a witch or wizard might not need that on a wristwatch, but perhaps there are other things (i can't think of any examples but the Weasley's) that would be useful? If your character wears a normal watch, one that only tells the time, it does not need to be purchased.
2.) The Herbology teacher isn't played yet, but I can't imagine there being a reason why the Herbology professor or Potions professor wouldn't lend him one. I wouldn't recommend Emmett going around telling anyone he's helping DJ do this, however.
Like I said, let me know if you have more questions!
[brid]Bridget[/brid]