There remains an open question as to whether Sage knows about the restaurant.
IMO, there are three possibilities:
1) She is blissfully ignorant;
2) She is willfully ignorant (i.e., she purposefully looks the other way and probably knows at some level what is going on);
3) She is fully aware.
I speculate that Sage might have been one of Stephen Burke's first girls propositioned to 'service' his clientele (perhaps not in an organized way like with Quinn's arrangement, but he might have encouraged her to use her looks to satiate his friends). This may be the main reason why Sage is reluctant go to her parents for help - i.e., she knows at some level that it could come with unacceptable strings attached, and is why she is willing to look the other way with respect to the restaurant.
Could be an interesting source of drama in future episodes!
Sage is Burke's daughter (adoptive but that doesn't change anything). Jade and Burke both work at B and R, and don't seem to be short of money, their daughter should have no problem paying for college. Why would Burke go prostitute his daughter (or even goad her into doing anything)?!!
I think there is on one side the restaurant and on the other side a thing for free tuition.
The restaurant is for students who earn some pocket money. The restaurant is not to pay for college, or else the girls should prostitute themselves 24/7, which is not the case.
Then we have free tuition. That's pure speculation there. We only have indirect clues. One can imagine that it is a system that diverts donations made to college to pay for a girl's schooling, and in return she becomes the sugar baby of an old pervert. (in my opinion this is what happens between Mona and Burke, he offers to find him a sugar daddy in exchange for a free tuition).
What does Sage know? In my opinion nothing about free tuition. For the restaurant, it's not presented in the game as sordid prostitution. It's borderline shown as a fun thing, students who link business with pleasure. So Sage could very well know it, and not find fault with it. Except she's the president of HOT, and if the scandal breaks out she'll be impacted, so I don't think she knows.