Okay, let me point out a couple of things to you ... since you are too young to understand how the real world works ... a "mental hospital" does NOT (repeat, they do NOT) simply take a minor child into lockdown because mom says she is crazy. It does NOT work that way. Not at all. It can be a real pain in the ass to commit someone. So, that story is either a lie, or they are leaving out some very significant details.
About your friend having no options - that is untrue. He was 18, he was an adult, he could choose to leave if he wanted to. He chose not to.
Now, maybe mom DID throw herself at him ... maybe. And maybe she DID threaten to go to the cops about him diddling her daughter. What does he want YOU to do about it? HE can go to the police and make a report for extortion and a sexual assault ... though he wil also face a potential felony for his own actions with the 15 year old. Or, HE can stay quiet, move out, and not do anything to avoid any trouble coming his way. The choices are all his.
You have your "serious" answers. Now, what does HE want to do? About all YOU can do is give him money for a new place, put him up in your parents' place, etc. And if he is asking for this, it may be that he is manipulating you and your friends for his own gain.
Another question, have you actually HEARD this recording? If so, he may have a strong case against her. But, again, that is still HIS decision to make.