Is there any bad effect on transplanted hair if I take gym supplement such as whey protein, pre workout and BCAA?

There is no bad effect of using protein for gym reasons. However using steroid especially long term use could cause serious damage. 

It is best to contact your doctor about post operative care and instructions since each doctor has a different regimen. Protein is not bad for your hair.

The kind of supplements you mention should be of no consequence. Of course testosterone/androgen containing supplements will tend to cause further hair loss as well as other medical problems and should never be taken without proper medical supervision and monitoring, and only for diagnosed Testosterone deficiency.

At one year, you are normal. The use of supplements that contain any anabolic steroids will negatively impact your hair so make sure that there are none in the supplements