It doesn't auto-close in all modes. Some leave it open so you can e.g. modify the selection criteria without worrying about it closing while you're still thinking.
That's a "feature" of Windows 10 and above, affecting pretty much all text input controls. There's a registry setting to change it.
Using a quick key, then escaping the FAYT field, and using a quick key again (same or different) does not clear the previously used quick key, it adds to it.
Escaping the FAYT field twice inserts a square character into the field.