Why is this in the present progressive, "is swimming" rather than in just the present "swims"?
No, it should be pronounced as a 'v'
If you are in doubt about pronunciation - the automated one here in duolingo often sound artificial like the syllables have been chunked together - I suggest to visit either www.forvo.com where users have recorded words themselves, or http://ordnet.dk/ddo (which is the official danish dictionary) where they are good soundbites as well.
Pronounced w's are only in lonewords with a w - like weekend. But often you can even pronounce w's as 'v' in the lonewords: http://ordnet.dk/ddo/ordbog?query=weekendsearch=S%C3%B8g
Thanks again Frederikbr!
Does your 'v'/'w' comment also apply to the word 'skriver'? Duolingo's TTS makes it sounds like it's pronounced "skri-ware".
Well, it seems I was i little too quick, when I wrote that w-sounds are only in lonewords. They are actually quite frequent. Sorry.
For me it seems that w-pronunciation is especially frequent in words where V appears in the beginning of an unstressed syllable like in 'skriver', 'over', 'bæver' (although not in cover where the English pronunciation is used). Since there are a lot of verbs ending in -ver in the present tense, you will here it a lot. However, in most word (not 'over') you can also pronounce it with a v-sound in standard Danish.
Also, syllables ending with a v or g, like 'hov' (hoof or whoops), 'hav' (sea), 'havre' (oat), 'magre' (meager), 'brag' (boom). Here you can only pronounce it with a w-sound
I think the confusion comes from the fact that w-sounds in the beginning of syllables (like in weekend or whip) are very uncommon in Danish, but the softer ones, where it is almost just like a syllable ending in a u are quite common (like in slow or laun mower)