Kann ich gewarnt werden, wenn einer Lehrkraft die für eine Stunde nötige Qualifikation fehlt?

Yes. On the Subjects screen, tick the “Required skills” a subject needs. If you then add a teacher to one of those sessions and they’re missing any of them, a warning appears listing which, with “Override” (add anyway) or “Cancel”. The check is for teachers only — adding a teaching assistant never triggers it.