In order not to forget the date （when）【he can play games with his friends】
括号内是定语从句,主语是he,谓语can play with,宾语 his friend,缺少状语,副词做状语,所以用关系副词when引导.
which是关系代词,用来做宾语.这里不缺少宾语.Will You hold on to studying?对不还是continuehold on to doing sth 没问题，语法是正确的，表示坚持做某事（不放弃的意思）与continue不同，continue doing sth 继续做一件事情（没有不放弃的意思）