can i visit a friend who is on student permit.? ln this case what proof of relationship can i provid

Selina, yes, you can, but you cannot apply for S type entry permit for private visit.
You can apply for a tourist L type entry permit to PRC to visit your friend. You can ask your friend to issue an invitation letter to you. Inn addition, you also need to provide your passport and its copy, the application form, and a passport-style photo.