Can bad teeth cause face asymmetry. all my left sided teeth are pushed in towards the tounge. can this cause the cheekbone to look sunken ?

Facial asymmetry: Just for your information, true facial symmetry is extraordinarily rare and almost never occurs. The most common causes are teeth, skin imperfections, and variation in the bone structure. Rec.: see an orthodontist (braces doc) for evaluation, cosmetic imaging, x-rays and treatment if needed. Take care.

Is this new or from: Birth? Some syndromes cause hemifacial microsomia (one side of the face smaller than the other). If you feel it's disfiguring or it causes a dental malocclusion (abnormal alignment of your teeth), see a maxillo-facial surgeon to determine if you're at risk for temporo-mandibular joint problems later in life. If congenital, a chromosomal microarray ; clinical genetic evaluation are warranted.

Yes, depending on: Extent of deformity. Also, maxillary teeth in bad repair can cause sinus problems. Have an oral or maxillo-facial surgeon take a look. It sounds like it is beyond scope of a general dentist.