He is right that he isn't in a position to date though. He needs to be focusing on his mental health and basics of survival on his own. You can be supportive of him, but that's about it.
If someone mentions plans of killing themselves like he has to you, for me that's an automatic call to 911. I'm not playing. That is beyond "let's chat and I'm hold your hand and listen, hon". Thats serious business.
I think too you need to consider why you chose this, you knew this person was not in a stable point in his life when you got together (living in his car!) yet you dived in anyways. Why? Is it because you are living at home and are scared if you date someone who is standing on their own feet they will expect that of you too? Time to get real with yourself here too.