Mona leaves and her card is deleted, then do this forcing to send away a girl who has no reason to stay
I don't know, but regardless of whether she can pay or not she still has no reason to stay
No, Mona has several reasons to stay, namely the friends she's made so far (definitely Camila, possible Maya and Josy) plus whatever reasons brought her to B&R in the first place. What's changed is that Mona now has a reason to want to leave: some combination of shame and guilt over what she did, or concern about Burke/Quinn taking preemptive action against her.
Interesting that when confronted by Jade, Burke admits to having had sex with three students. Seems to be a small number. Either he knew he couldn't say lower, jade wouldn't believe him, so he went with a relatively low number compared with reality, or else he hasn't been using the girls that much. I felt it was more a service he was offering to other wealthy men in the community.
He admits to having sex with three students, not necessarily to having sex only three times with students. A significant distinction if it turns out he is providing ongoing funding through bogus scholarships.
If there are scholarships in the books to explain how the tuition is paid for these girls, then the money would have to get paid, otherwise the college would notice the missing money. So Burke would either having to be paying out of his own pocket, or it's a scam scheme that gets charitable donations to pay for it. Either way, Burke would have to ensure that payments are made.
Or Burke is hiding the loss through accounting legerdemain. That would normally require someone on the admin side rather than a "professor," but Burke's actual position is very vague and B&R has a weird structure anyway; if Cathy can teach both Math and English, Burke could potentially be both a dean and an accountant.