A lot of what has written concerns me and I understand that you are not his Mum, but it is still worrying.
I know she has ignored your suggestion of going to the GP and getting a referral to the CAMHS and it's possible she is burying her head in the sand. A lot of people hold a stigma to mental heath, they don't want it to happen to them or they are scared because it is naturally a scary thing to face.
I find it sad how alone this poor boy is. He is only 14 and even though we all probably felt pretty grown up then, he isn't.
At 14, I was self harming and depressed. By 15, I was intent on killing myself and eventually admitted to hospital.
Nobody listened to me BEFORE it got that bad. It was not enough to be depressed. The help wasn't there and I ended up in hospital because it escalated, which has gone on to affect my life.
I appreciate you can't do everything his Mum can but if your sister won't do something, can you not fire off an email to his school and make sure they are aware of how he feels and the things he has stated/you have been told of.
It would be awful for him to keep slipping through the net and I know how much worse it can get.
At least once the school are fully aware, they can look at putting support in place there and arranging for outside agencies if needed.
I am sorry that this is all so hard. I can imagine it is very difficult with four children of your own, and trying to work out how to help here but please don't shrug it off. He could be basically screaming out for help and hoping that someone will hear him.