I do discuss most of the topics you raised in the second half of my post.
On #4, I agree that would make a lot of sense, but I can't reconcile that logic with the way Chad acts towards Sage in the Episode 5 flashback (complete disinterest once he establishes the HOTs only party with the jocks), and when he asks Sage for help in Episode 3 (the peck on her forehead). Neither of those do much to keep Sage at his side.
The Episode 3 case is particularly bad, because that's when he is visiting Sage specifically to beg for a favor. Even if Chad wasn't gay, his treatment of Sage makes no sense. If there was ever a time to butter her up, you'd think that would be it. But he could only have acted like less of a boyfriend if he'd pinched her cheek.
So I'm forced to conclude that Chad isn't interested in keeping up the idea that Sage is his girlfriend, whether she's a beard or not.