Having reread your post numerous times, please allow me to comment on some of your key statements:
>>From what I’ve been told, people with this illness can often impulsively do things that involve no longer taking medications, violence, risky spending, etc.
I am not aware if the ex or her family understands the full implications of this.<<
Not your job, or the job of anyone giving a shidduch reference to educate the other party as to the potential issues with the condition.
e.g. you can say the girl has cancer in remission, but you cant go into detail as to what that means. You can only give the facts, the person doing the inspection, they themselves need to research as to what those facts mean.
Nor is it your place to educate them as to whether or not they truly understand the “full implications of this”.
>>Furthermore, a rav who knows him told me that this guy is “in pain,” “vulnerable and manipulative,” has “bad relationship ethics and an unhealthy attitude towards relationships, sex, and marriage,” and he said that “no one’s mother would want their daughter to be with this guy.”<<
Then this guy should say something. If he has, then nothing you can do. If he hasn’t get him to say something.
What on earth are you going to say exactly? “I don’t know this guy but I hear he has major issues?” really? c’mon you have no proof, you know nothing 1st hand. Sounds like Loshon Hora (forget L’Toeles, you have no proof it is true, all you have is hearsay).
>>Knowing this, what should I do? Especially that I am friends with the girl’s aunt and cousins, who have been very good to me materially and in other ways.<<
This plays no role. You should do the same thing irregardless of whether you know the girl or not, her family or not. There arent 2 sets of Shulchan Aruchs, 1 for friends and 1 for strangers.
>>I feel that I have an achrayus to say something and not saying anything would entail an issur of Lo Saamod.<<
Sorry, the only people who have an achrayus is those who know, not those who have overheard. You can encourage those who know to share what they know with the necessary parties, but other than that, move on.