By the way, I'm pretty sure this only refers to loudness/decibel level and not to other English meanings of volume (e.g. volume of a substance in liters, a volume of writing).
Yes, indeed. The word "lydstyrke" literally means "sound power/strength"
You are right "volumen" can also be used for size (liters) and sound in danish (just like english but why teach the simple translation) but is mostly used for size
It would be a more effective question to ask "...increase the volume" or "...decrease the volume" rather than necessitating a follow up question as to changing the volume in which direction. Just saying.