Is bell's palsy a hereditary?

No. Bell's palsy is thought to be due to a viral infection of the facial nerve. Other causes include lyme's disease and sarcoidosis but its is not passed down from one generation to the next. That is not to say that you would not see bell's palsy in a parent and years latter in their child. Bell's palsy rarely is seen bilaterally, if so it is diagnostic of multiple scerosis.
No. Bells' palsy is an acquired condition that causes weakness or paralysis of the facial muscles and may be related to a viral infection. There are inherited causes of facial paralysis but these are not true bell's palsy.