Will a sliding genioplasty and a septo/rhinoplasty keep my mouth closed at rest? (Photo)

I believe, your xray shows mild case of vertical maxillary excess, which means your upper jaw grew down too much, pushing your lower jaw down and back. chin surgery helps you to close slightly, but jaw surgery is preferred to improve the over all aesthetics.

A rhinoplasty is performed to cosmetically change the shape of the nose. A rhinoplasty will not improve breathing out of the nose. A septoplasty  repairs a deviated septum, once medical necessity has been documented. A septoplasty will not change the shape of the nose.  There are many reasons patient's have nasal obstruction and keep their mouth open, which include a deviated nasal septum, valve collapse, vestibular stenosis, turbinate hypertrophy, chronic sinusitis, and allergies. Each one of these is treated differently with either medications or surgery to improve air flow through the nose. For many examples  and more information, please see the video  and link below

A sliding genioplasty can improve mentalis strain and lower lip incompetence, particularly if the vertical dimension in decreased and the horizontal dimension is increased. A septorhinoplasty will improve nasal airway breathing and may decrease mouth breathing but will not improve lip incompetence.