"Where to does the duck swim" - is this not also grammatically the same?
My understanding is yes; In general, Swedish makes less distinction between the simple present and continuous ("I swim" vs "I am swimming"), just using the present for both. Later on there's a module on Continuous forms for when you need to emphasise that something is going on right now or is continuing to happen. I think Duo always accepts both versions (e.g. "Jag läser snabbt" should accept both "I read quickly" and "I am reading quickly").
Unfortunately, I can't think of a better way of getting across the distinction between var and vart.
Personally, I don't mind ending on a preposition- to my mind, "poor grammar" is something that is not clear and natural, and all the alternatives I can think of are ambiguous ("where is the duck swimming?") or unnatural ("Where to does the duck swim?"). I have no idea if Duo accepts "Whither swims the duck?" but I suppose that would have been the traditional answer.