I'd rethink the reply to her email. Asking "are you sure that's what you want me to tell S" comes across judgmental and critical. Nothing positive comes of that.
Instead control YOU. How you respond to it. You have choices. You can pay S's language exams out of pocket. (I just had this EXACT situation come up and I mentioned casually "I paid the enrollment because we don't have an official agreement in place on how we handle these situations, I'm sure we'll have something nailed down soon so we have a template to follow", this allowed me to do what was right for my S without acting as if I set a precedent that I'd just take it in the shorts perpetually.) You can take it out of his savings as she requested. You can not do the exams. Those are the choices. But trying to control her or influence her decisions with criticism and judgment is not going to be productive.
As for the emoji icons and back handed sweet talk, yeah, XW still does stuff like that. It is all about their internal narrative, the one in which they are good loving people, victimized by circumstances and forced to destroy a family. Like you I have been unresponsive. I'm sure in their mind that is fuel for the fire (they are trying to keep things amicable, we are being distant and hostile, etc). But their narrative doesn't mean a darn thing to me. Sure, we're the bad guys, they're the mature better people. Totally fine.
I just remind myself I only have to deal with this crap for a few minutes a month in an email. She has to live like that. I sleep soundly at night, thank you very much.
Hang in and keep posting.
Me:38 XW:38 T:11 years M:8 years Kids: S14, D11, D7 BD/Move out day: 6/17/14, D final Dec 15