You're gonna do great on the webcam encounter, T. If you're getting As on exams with everything going on, you're seriously superwoman. Be confident and don't forget to suck up if you have the opportunity ("thanks so much for your feedback. I really focused on what you said and I hope I showed improvements.")
A friend of mine is having an argument with her H and he's not talking to her and she's like "but then I think how you dealt with this for weeks and I think it's not so bad." I corrected her that it was months I was dealing with it.
I second Train's suggestion. If H is around, nonchalantly ask if he'd take a look at the dryer. He may refuse, but you'll be no worse off.
There's no instruction manual, T. The basis to guide how you conduct yourself is that you're doing it for you. If you don't feel like talking to him, don't. If you feel like saying a polite "hi", say it. You don't have to ignore him and his texts, but you also don't have to answer them (if they're not necessary about the kids.)
You've been so focused on watching his every move for months that this should feel like a relief to you - you just get to do what you feel like and you don't have to care what he thinks. (Though I'd still remain somewhat detached and avoid arguments or R discussions like the plague.)