So "volymen" can be used to descrive how loud something is or how much space something takes up?
Yup, just like in English. Actually, I noticed that quite a few senses overlap, so I took a look at Wiktionary's English entry for "volume" and realised that all eight senses are possible in either language. :)
Does volymen refer to just a measurement, or both the measurement and how loud something is?
Volym can be a three dimensional measure or a sound level :). Here, it means sound level. When talking about the three dimensional measure, "volymen" är "stor", not "hög".
Tjock-tv:ns volym är stor.
And it actually is an accepted translation. Maybe it was given as a "type what you hear" exercise? Duolingo still won't accept alternate spellings when they're pronounced the same, it's like that in all courses and it's terribly annoying.
As far as I know, in the French course it is allowed. But French has a lot of words that are spelt differently but pronounced the same so one sentence can often be interpreted in several ways. Maybe Duolingo allowed it just for the French course.
That's quite possible. I don't know about this specifically, but I do know there's a big difference in how the so-called in house courses (such as French) work vs the incubated ones (such as ours). Anyway I've disabled the dictation exercise for this sentence now, we've already done that for a number of TV sentences for this reason.