I don't care about my boyfriend's friends depression
How could not not care about his depression?
I don't even know him, so I don't have to be the one caring about him.
It can be tiring caring for others. But as your boyfriend he deserves your compassion and patience anyway.
I should tell the school counselor in case that friend might commit suicide.
It's a great idea to reach out to an adult about that friend's depression. No one deserves to go through such trauma. He might need a lot of help trying to set things straight.