Is the German wife still a legitimate wife to the man after she was divorced in absentia in both Germany and Algeria, and after the man had verbally divorced her several times before that, and is this considered an exceeding of the three divorces, given that the first wife knows that she returned to him more than once?

If the husband pronounces or writes down a divorce with the intention of it, then it becomes binding. If the husband initiates two divorces in court, and this was preceded or followed by a third divorce, then the wife is irrevocably divorced and is not lawful for him until she marries another husband. A mere agreement to divorce is not considered valid unless the husband actually pronounces it.

If the husband did not divorce her in the two instances in court, he may reconcile with her before her waiting period (iddah (definition)) expires. If her waiting period has expired, he may return to her with a new marriage contract. Anger does not prevent the divorce from taking effect, unless it reaches a level where the person loses perception and awareness.