Donor area is red and dehydrated. Can I use a moisturizer? Is it OK to rub the transplanted area after 2 weeks? (Photo)

Redness 2 weeks after FUE is not typical.  You can resume normal sleeping.  However, it is always a good idea to check with your doctor for your issues.  You should read over the post operative instructions or call your doctor if you are not sure.  

The donor site will heal quickly. Using a ceramide based moisturizer may be a good idea. In our office, we recommend Elevase Moisture Booster with opto-ceramides. Best, Dr. Karamanoukian Los Angeles

First I would suggest that you go back to your original physician. Redness can be a sign of infection. If it's not an infection, it could be redness due to early healing.

Hello.  We all have different protocols for recovery after hair transplant.  Your questions are common and should have been detailed in your post op instructions.  I would suggest following up with your doctor to see what his/her protocol is.

You should see your doctor. Although I am not particularly concerned at what I see, you are and a hands on examination is what I would do if I were your doctor

After FUE, the donor area goes through a healing process by secondary intention. That means a small crust is formed that can last for up to four weeks. In this period, keep the area well moisturized. It is ok to use a baby shampoo and gently rub the area. After washing, quickly moisturize the donor area.