Asking a person if they feel suicidal will plant the idea in their head. Helping someone to acknowledge their problems is a first step in solving them. Your expression of concern might help them to feel better about themselves. The stress of being a college student makes suicide more likely. A drunk person who talks about suicide should not be taken seriously.
Suicidal students are mentally ill.
Not necessarily although the likelihood of actual suicide for students with deep depression is four times that of their non-depressed student peers.