The Zeeland coin is listed in my Krause as a 2 duit piece. I concur about the date being key to identifying the portrait (and vice-versa). I would also concur about the date being 1604, meaning the portrait should be that of Philip II. I couldn't find any online pics of either type to compare it with.
The Wilhelm II and Frederick medal would indeed be a souvenir piece. I suspect the medallist made the Frederick obverse originally for a souvenir coronation medal, and used it again on this piece when Frederick died shortly after becoming emperor.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis