Does scalp hair grow faster than beard hair?

This indicates poor washing. You must wait until these scabs fall of with gentle finger massage during your shampooing process. 

Typically, unless you are using a device like Capillus 272 or Laser Cap, the new hairs that were transplanted go into a resting phase. You should start seeing new hairs growing again at about month 3 to 4 and then improving every month up to about 12 months.We typically have patients come back ...

This can not be treated with a hair transplant because any active disease will kill the hair transplant. An alternative treatment that works terrific is scalp micropigmentation (see sdb site below)

The reason/s why you shouldn't bend your head at least the 1st day post op so you will not cause grafts to pop out or an increase bleeding in the recipient area.  

If you see a doctor, get the diagnosis (probably genetic balding) you can have FUE. The use of Propecia is to prevent shock hair loss, something that happens to younger men. At 35, your chance of getting shock loss is less, but nevertheless there. See video below

Accutane will kill the hair grafts. You must wait at least 8 months before going back on the Accutane. That also applies to people on the drug before a hair transplant as they need 8 months without the drug before having a hair transplant