Hey OP, I think your expectations are perfectly reasonable. And letting her know that if they are in your way you are going to move them, is also perfectly reasonable (yes, the texting is getting crazy and yes, sounds like lots of bickering and an overall bad situation). Now she says don’t talk to her and only contact her through a groupme? Yikes.
I think if I were you I would just move them to a basket. Don’t talk to her about it. Her asking you not to touch is not right if her clothes are in your way, on your day. I wouldn’t fold them…first of all she doesn’t want you touching them in the first place and second of all, she is being inconsistent and bratty and inconsiderate of your need to do laundry. And honestly given this situation folding them would be downright weird.
Honestly things just sound really bad with the roommate…texting isn’t solving anything and it just doesn’t sound like any in person communication is going to happen. I guess do what you can to let their brattiness roll off your shoulders. Focus on things besides your bad roommate situation, if you can.
And yes putting underwear in the kitchen sink is disgusting and not to mention a complete inconvenience to make the kitchen sink unusable for anyone else!