Yes, a sinus infection can cause a toothache. Your doctor can give you antibiotics that will clear up the infection and should take care of the toothache. It does take a few days, however, for the pain to go away.
Yes. It depends on the type of sinus problem. Saline solution sprays at a pharmacy would probably fix it. If it is causing a toothache with a wisdom tooth (like I have), I would suggest getting the wisdom tooth pulled.