#3. "Can you watch my bag for a moment?"
A really bad idea. It's not that librarians are inherently untrustworthy people, but the fact that libraries are actually not nearly as secure as you think they are. Theft is an ongoing problem in the library environment -- not only are books and periodicals targeted, but computers and other electronics, as well as the personal property of staff and unsuspecting library patrons. And for the love of Melville Dewey never, ever leave your bags (or worse yet your laptop) unattended while you go back to the stacks, take a pee break, or step outside the library for a smoke or a bite to eat.
My rule of thumb is: if you wouldn't feel comfortable leaving something in a crowded train station, then by all means don't leave it. And don't assume that academic libraries are somehow immune to criminal behavior -- while working at the Circulation Desk at one of the subject libraries at MIT, I had my wallet lifted from my backpack (which was kept out of sight behind the desk) despite the fact that the Circ Desk was always manned by at least one person at all times. If anything the aura of safety projected by a college campus encourages such "crimes of opportunity."