Can I sue my ex-girlfriend for rent, because she gave me no 30-day notice?

You can't sue her, and she can't sue you.

You don't have any sort of a contractual relationship about sharing the rent, unless you are one of the very rare couples that puts this sort of thing into writing.  So you don't have a landlord's remedies here.

Gifts are given, or they're not gifts;  your ex would have to convince a court that the things she wants back weren't given to you, they were just loaned or something like that.  If she moved out without them, it's going to be very hard for her to persuade anyone she still thought of the items as hers.