Better inform the grad student. If there is a error, probably the reviewer will find that as well while reviewing the paper. So earlier he/she knows, the better.
Yes. You don't have to send your SOP unless they ask for it. CV is enough. I too don't know what they ask in the reference form. Try to find if there is template of reference from the university if they accept manual reference letters
I sent my resume and also gave them details of the work I had done with them - courses/research projects/TA and grades obtained.
Send you CV to your professors.