Can my sinus infection be the cause of my toothache? Is yes, why? I have a dentist appt in a few days...Should I mention the toothache if b/c sinus?

Yes. Sinuses are so intimately involved with your teeth so often soreness with biting and cold sensitivity accompany a sinus infection. Your dentist should do some vitality tests and surmise whether your pain is from sinusitis, fracture, cavity, or some other source. I hope you feel awesome soon. Toothaches are no fun.
Yes and very common. We see it all the time. Someone has a sinus infection or even cold, allergies or sinus inflammation and they have related tooth pain. This only happens with upper back teeth as the roots of those teeth border the floor of the maxillary sinus. When the sinus problem is resolved, the tooth ache also goes away. However, you can have a dental problem totally unrelated so it must also be checked out!
Yes. The roots of upper back teeth are in close proximity to the maxillary sinus. It is possible for there to be some referred pain as a result. This is also why an infection on one of those teeth will occasionally present with sinus symptoms. Mention the recent sinus infection to your dentist. It may or may not be related depending on what tooth is in pain.
Possibly. It depends on which tooth aches. Only the upper teeth can be in communication with a paranasal sinus. As such, if your lower teeth hurt, it is not likely to be related to your sinuses.
Yes. Consult a physician. If it is diagnosed as sinusitis then antibiotics will resolve your symptoms.
Yes & yes. The sinuses sit just over the upper teeth, so pain can be misinterpreted as coming from the other. Also, due to proximity, not impossible for infection to spread locally, but less common. Should still see dentist, since can also have two things going on--just tell dentist about it.
Yes and vise versa. If your tooth problems are in your upper jaw, then it definitely could affect your sinuses. The roots of the teeth can infiltrate the sinus cavities from below and can cause problems. A ct scan could show this and you should also see an ENT for this if it continues.