1) Just don't.
2) If you know her circle of friends, then it shouldn't be too difficult. Doing a little homework about a girl you're interested in isn't stalking. Especially if you have overlapping circles of friends. Just don't end up uninvitedly in her closet or outside her window.
3) Obviously you wouldn't wear the watch. Carry your cell phone and keep it in your pocket. Or if you insist on a watch, keep it in your pocket unless you're at work or not asking girls for the time. All you're required to do is ask the time, it should take no more than 10 seconds. You'll either get one of two answers, they will tell you the time or they won't. All you have to do is say "thanks" and make your exit.