I got Full Facial Hair transplant 4 months back. Normally hair is supposed to fall in a months time. For me it didn't.

It is normal to lose transplanted hairs weeks after surgery.  It may take 6 to 12 months to see new hairs grow out.If your hair didn't fall out the way you thought it should or you have red spots, you should contact your doctor for a follow up exam.

Regrowing hair is thin, undersized and not bright untill 4-5 th months of hair transplant. İt's normal for new growing hair starting to get native characteristics, waviness, curl in first 4-5 months..This actually takes 10-13 months for hair to become full mature , as thick and bright  as native hair. 

That pinkish redness/discoloration may fade away in a long time up to 3-4 months . İt depends on your skin color/fitzpatrick classification (Lighter the color of your skin , more reddish discoloration on skin after surgery). I recommend you to use nothing for that temporary situation

If you are experiencing any complications after a hair transplant you should return to see the doctor who performed the surgery. Red spots around grafted hairs could represent infective or non-infective inflammation.Transplanted hairs to the beard area might not look as normal as natural hairs when shaved. You should have been warned about this when considering the transplant. Beard transplants look best when the beard hair is grown a few millilitres at least.