Honestly, it doesn't sound like a healthy relationship for you to be in at all. It's hugely damaging on your self-worth and general mental health to be treated the way you've described. If he cannot cope with the long-distance, it's not your responsibility. For your own health and happiness, you should end the relationship and move on (I know it's hard, but it's better in the long-run, trust me!).
If you're worried about his mental health, maybe you could reach out to one of his family members or his university. If he threatens to hurt himself, do not react to this - just call the police in his area and explain that you are concerned for his wellbeing and outline the situation. I understand it being an incredibly awkward and stressful situation for you to be in, but it's important that you always put yourself first. You clearly have not entered into a mutually open relationship, so you do not have to put up with being cheated on and you have absolutely no responsibility to forgive him and move on. You are absolutely entitled to feel upset, hurt and confused. Please don't let him carry on treating you like this. Nobody deserves to be cheated on!
It's also unhealthy for you to do "tests" like posting a picture of you and another boy, it'll only serve to mess with your head more in the long term. His reaction to this also shows how little regard he has for anyone but himself because he demands emotional validation from you when he feels threatened in the relationship, but sees no issue with openly telling you that he has no respect for you by flirting with other girls and requesting a FWB relationship with someone else. You should get out of this relationship before it makes you feel any worse!