It is always best to hang from a solid structure like a stud. This does away with ever having to worry that the fixing in the plasterboard is strong enough. There is a variety of products to hang the mirror with and it depends on what type of fixing it has on the back.
It sounds like you might have either a calibration issue and/or a faulty stud finder. The process normally involves holding the stud finder on the wall and turning it on and/or holding a calibration button.