Is beard transplant for life? I mean permanent?

Transplanted hair is considered be to a  permanent solution.  The hair should be taken from the back of the scalp where the hair is genetically predetermined to last. 

Beard transplant is considered permanent as long as the donor hair is from a permanent area.  The back of the scalp in most men is considered a permanent area.

Yes, whether it is scalp hair, body or beard; transplaknted hair follows the characteristics of the donor area.  Since we don't expect to lose our beard by aging, beard to scalp hair transplant is considered permanent.

Yes, like hair transplants, beard transplants use hair from the back of the head where the hair will grow the lifetime of the person.