He was apparently in a "special housing" area of the institution, the same thing as protective custody. I would think it unlikely another inmate could get to him.
I don't know how it works in New York, but here in Tulsa it would be very unusual to keep an inmate on suicide watch for six days. After three days he is evaluated by the psychiatrist and either returned to a housing unit, or transported to a psychiatric hospital for further evaluation and treatment. I would imagine the psychiatrist at Epstein's institution is going to be answering a lot of questions.
Onward and upward,
airforce