I had a beard transplant a day ago. How much time it will take to get the full beard? When will the red spots go?

You should make an appointment to see the physician who performed your bear transplant. You possibly have folliculitis that can be treated using oral antibiotics or topical meds. If you cannot get back to the transplant surgeon, then definitely make an appointment to see a dermatologist.

Follow up with your doctor if you are concerned about your scarring or "marks".  It may or may not be permanent.   It may take several more months for it to fade.

Beard hair is a genetic trait.  There is no medication to grow a beard.  Some try topical minoxidil but you would need to use it everyday and there may be side effects.  You should see a doctor before starting such treatment.

The redness should slowly go away and be gone in one - two months. Some people get more red than others. 

It may be worth trying minoxidil. 10% is a specialty order item and I don't have much experience with this concentration. Most doctor feel that high concentration may work better but there are more side effects.

Facial hair growth is a genetic trait.  If you have very little facial hair there isn't much you can do to increase the growth