vill is the present tense and (att) vilja is the infinitive. Like want/wants vs to want in 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 It's merely an outdated way of speaking, as it avoids splitting the infinitive - a tendency to which most people are no longer inclined.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".