I agree with your friend. I would not bring up the "dating" topic. I would only suggest having an answer in case it were brought up.

It sounded like you did a great job "acting as if" when he was over there while you got ready for work. Truly... I'm just any other guy and if there's a woman who is almost half naked getting ready in front of me... Unless it's a relative... I'm gonna be paying attention to that person... but who knows why he appeared attentive to what you were doing or "how"... At least he appeared to "be there" in the conversation. That's always a plus.

I wouldn't worry too much about the "y'all" comment. If he has some issue about that, it's his problem. If you are not complaining about his time with the kids, then he's just making stuff up in his head that he has to work through.

There's nothing for you to apologize for regarding what he may think you have a hand in. As much as it sux, if you acknowledge that you are aware things are being said to him that upsets him, he will think you have something to do with it. Even if you say you don't. So your doomed if you do and doomed if you don't. You're probably best to just leave it be.