Would this work? "He seems not to want to listen."
Yes. Duo should have that translation if it doesn't have it already.
Could someone please explain the difference between "vill" and "vilja"?
vill is the present tense and (att) vilja is the infinitive. Like want/wants vs to want in English.
It is not. It is very broken english.
Incorrect. It's merely an outdated way of speaking, as it avoids splitting the infinitive - a tendency to which most people are no longer inclined.
Avoiding splitting infinitives was never really part of English anyway.
Whether or not it caught on, the practice is not inherently incorrect, just a little janky. I remember my Latin teacher trying to convince the class that it sounded better as "boldly to go where no man has gone before".
Normally we would not give him the benefit of the doubt and just say, "He doesn't want to listen"
This is one of the example where the Swedish sentence is much leaner than its English translation.
Why wanting instead of to want is not acceptable?
"he's wanting" means he is lacking something. For example "he was tested for courage and was found wanting."
The verb "to want" as in "to desire" is never used in the progressive form, I believe.