Is it possible to get a seizure while under anesthesia?

Unlikely. Many of the medications used in anesthesia--especially those in the valium family (benzodiazepines)--actually work to prevent seizures. If you have epilepsy, be sure to tell your anesthesiologist and take your medications on schedule before surgery with a sip of water. None of the anesthesia gases or other medications in current wide use are likely to provoke a seizure.
Yes. Although rare, it may happen as a reaction to the meds or as a random occurance.
No. Most general anesthetics are actually protective against seizures. In cases of status epilepticus they actually use anesthetics to break the seizures.