Is it possible for a brain tumor cause facial paralysis?

Yes: But your doctor may be able to discern the difference between a central viith nerve and peripheral. The former could be from a midbrain tumor, but there are other central causes, the latter can be anywhere along the course of the nerve after it leaves the brain stem. The most common cause is bell's palsy. Discuss this with your physician.

Yes, but not likely: Brain tumors near the brainstem can cause facial paralysis but that is not a common cause of facial paralysis. This would almost always show up on an MRI scan. See your doctor for evaluation.