Some people are radiators. They give out warmth, interest, positivity, even if they're not necessarily feeling it.
Some people are drains. They suck all the joy out of the world, complaining, moaning, bringing everyone down.
Sadly, she has been a victim of her mum's drain tendencies and doesnt do anything to turn herself round.
You don't want this to happen to you in turn.
I'd send a frank message saying you're concerned about her, she's obviously aware she has mental health issues and needs qualified help. Suggest she go to a GP, maybe seek some therapy. If she is clinically depressed there may be help there. Stress it's important she does some self care.
But it looks like she may be very difficult to help in her situation. She has to want to get out of it instead of wallowing in and moaning about it, blaming it and resenting you your life. It's obviously having a negative effect on you and you don't need it.
Incidentally, she isn't a friend - she's an acquaintance. There's a difference. Stop resenting that she doesn't like your stuff on Facebook. Stop looking at and responding to her messages. Maybe check in every so often - and repeat your message, refusing to be drawn down her drain.