FUE hair transplant exactly a month ago. Accidentally scratched scalp and saw hair graft coming out. Is it my transplant graft?

It is best to ask your surgeon about post operative care as each doctor has their unique regimen.  If you had bleeding then some grafts may have dislodged. There is no way to tell based on a photo.

It is best to ask your surgeon about post operative care as each doctor has their unique regimen.  Dead skin will not affect your results.

It is best to ask your surgeon about post operative care as each doctor has their unique regimen.  Drying your hair or keeping your hair wet has no impact on hair loss or hair growth.