Here's the timeline as I see it:
- Saturday night, Week 2: MC drives Cathy home, fools around with her but leaves her panties in the car.
- Tuesday afternoon, Week 3: Bella helps MC clean his room at the DIK Mansion. (No mention of panties)
- Tuesday, Week 4: MC works at the library with Bella, resulting in the LiBrian scene (No mention of panties, but Bella acts differently depending on the panty scene).
- Saturday, Week 4: MC and Bella play tennis with Jill and Tybalt. Bella will finally mention the panties.
So to make sense with the events we see, Bella would have had to overlook the panties for the first three-ish days, then find them within the next 6. That's seems plausible to me.
I did think it was odd Cathy insisted on taking her panties off when the MC didn't do much to her. Now we know why.
This is why get nervous when Maya keeps saying she deleted the video of her threesome.
No, creating a blanket rule and applying it to everyone is precisely how the school would defend itself from accusations of bias against a "protected classes." They need only argue that allowing any students and teachers (male or female) to have sexual relations creates obvious conflicts of interest and thus it is reasonable to forbid them entirely.
vogelbeest already gave you a link to Yale's policy, and you can find similar ones with minimal effort.
Obviously B&R would need to have an actual policy to that effect to fire someone for violating it. But there's no reason they couldn't, and based on both Cathy's and Jade's comments, it seems likely they do. If you think it would be easy for Cathy to successfully sue B&R for such a firing, I invite you to find court decisions in favor of a teacher in similar circumstances.
Before you repeat that it's a school policy and not a law, so what? Being fired is generally regarded as a fairly serious consequence. The fact that a teacher wouldn't also do jail time is simply failing to add further harm.
Also, I think your understanding of civil rights is backwards. Protected classes were created by statute, not the Bill of Rights. Someone who sues an employer for discrimination is actually counting on the government to restrict the freedom of association of the company that fired them. One possible defense against such a suit is to argue that the legislature in question had no authority to pass such a statute in the first place. Something similar happened to large portions of the voting rights act a few years ago (though obviously that did not start with a matter of employment).