Is toothache a common problem for person with trigeminal neuralgia?

Yes. Depending on where your neuralgia is located , your pain can feel like it originates in a tooth, even if the tooth is healthy. A dentist can test a tooth to see if there is indeed pathology. Also, there are medications used to manage pain from tn that may help you .
Very Often. Trigeminal neuralgia often mimics as toothaches. In fact many people have root canal treatment and extractions of teeth wrongfully, because the dentist misdiagnoses the neuarlgia as pulpitis (inflamation of the nerve of the tooth). Make sure that you get different opinions if your tooth does not have significant amount of caries prior to getting root canal treatment.
Referred pain. The pain from the attacks can indeed be experienced in the dentition, but the attacks from trigeminal neuralgia are brief, a few seconds with subsequent residual aching, and not caused by dental conditions. The pattern is very identifiable, but, on occasion abnormal dental problems may co-exist and these too need treatment.
Possibly. Trigeminal neuralgia is a condition that is effecting the nerve that banches to all the teeth. In addition it has branches that go to other structures in the facial region. The location of pain can be felt anywhere along the entire nerve. A well trained endodontist should be able to differentiate a tooth infection from trigeminal neuralgia. Call your endodontist for assistance.
Of course. Trigeminal neuralgia is a painful neurological condition which is often confused with a toothache, leading to unnecessary dental treatments and teeth extractions.
It can be. Here is a website that lists all the symptoms that may be associated with trigeminal neuralgia: http://www.Mayoclinic.Com/health/trigeminal-neuralgia/ds00446/dsection=symptoms although shooting pains from the teeth might be related to tgn, one cannot assume that is the cause, and therefore it needs to be evaluated by a dentist to make sure nothing is overlooked.
Yes, unfortunately. Tn is a horrible problem especially when it masquerades as tooth and/or mouth problems. Please consult a neurologist who specializes in tn. There are also some wonderful pioneers with incredible results in decompression surgery for tn in pennsylvania. Make sure your toothaches are not caused by internal tooth problems by keeping your dentist informed of your tn condition. Best of luck!