If you get facial hair transplant from your head to your beard, will it be the same color?

Transplanted hairs will look and grow like hairs from the donor area.  So the color and texture may not match.  This is something you discuss with your doctor.

Barring an occasional random exception, transplanted hairs keep their original characteristics: color, texture, length, thickness, etc. So if the hair on your head is significantly different than your facial hair, it will probably look weird to transplant between the two areas.

Yes, If you have a facial hair transplant such as a beard transplant you
should expect the hairs that have been transplanted to retain the same color as
well as texture. Keep in mind, the transplanted hair will grow much like they
did when it was in the donor region. If your concern is
graying,  rest assured you may dye the hair to match the surrounding
hairs. 

This would depend on the donor region from which your follicles were extracted from.  They will genetically be the same as from where they were extracted and although they will change some in after the first 2-3 years post transplant, their color will remain the same.

Yes, the color of your hair should match and act like where it is taken from. So, if your hair is blonde and it is transplanted to where it is darker, it will grow out blonde!

The hair on the head remains the color of the donor area when it is transplanted to the beard or elsewhere on the body