This is definitely not true and people have gotten into a lot of trouble with it. Exactly what the conditions are varies widely from state to state and sometimes by locality, but if someone is living in a dwelling for an extended period, especially if they’re paying rent and having mail delivered, they can legally become a tenant without any explicit agreement from the property owner. People have found that they are not actually able to call the police to kick out what they thought is a guest who overstayed their welcome but the courts think is now a tenant. If you’re going to have someone live at your house for more than a long week (that is, from start of one weekend to end of the next) you should definitely check your local laws to make sure that you’re not going to have a problem if they decide to stay longer.
Since the OP hasn’t returned and we’re all just speculating, I’ll mention that it did cross my mind that perhaps “she will throw away what she feels I don’t need” meant drugs or drug paraphernalia, or that “She took my vehicle that was in my name” meant that she took the keys so OP wouldn’t get a DUI.
Absolutely not claiming this is the situation, just that it’s one of many possibilities.
That’s certainly possible, though not really the read I got from the situation. If the OP is using illegal drugs or drinking and risking DUI, then trying to get a court to intervene is… a much worse idea. In any case, I don’t think that getting the courts involved will have a positive outcome for the OP, it could cause her mother to blow up, and it could get her into a lot of trouble (depending on what they’re not telling us).
One reads stories from time to time that are much worse than that. Stories of people coming home from a vacation only to find that squatters have occupied their house (and sometimes even changed the locks and/or sold all the furniture), and only a prolonged court battle can get them out.