FUE: 1 week post op when can I have sex, if I can't sweat? Also, is sun exposure safe?

It is best to ask your surgeon about post operative care as each doctor has their unique regimen.  There is no restriction to having sex after surgery unless your doctor advised against it.

After the hair transplant operation it is very important that you do the right aftercare. The patients need to stay away from sexual intercourse least for a week.  Do not expose your head directly to the sun. Wear an appropriate hat.

you may have sex after 1 days of surgery unless your partner hit or rub your transplant area during having sex... , those are all wrong  advices .. sweating does not effect you implanted hair grfats .Exposing the transplanted hair to direct sun for few seconds do not make any harm , do not worry.