I have been reading about using Minoxidil for beard growth? Does it work and how should I use it safely?

If you always had patchy areas on your beard it may be normal. If you are seeing patchy hair loss on your beard, it may be a medical condition such as alopecia areata.  See a doctor for a proper examination.

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 indefinitely.  

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.

Beard hair transplant is a good option for your to grow hair in the area where the hair is not growing. It is a meticulous procedure therefore you need to chose your doctor very carefully. In the hands of a skilled surgeon it will look very natural and yields good result. 

You can probably shave after the scabs have fallen out and the area has healed. Always check with your doctor first.

Beard or facial hair is a genetic trait. There are no medications that will grow a beard.  Some may try Rogaine but if you do see results it is temporary.