It's not a literal translation but I feel like "Turn it down!" Should be an acceptible answer here. Especially with the exclamation point. If volume needs to be lowered urgently, "Turn it down!" is what you usually yell.
I think your sentence would be closer to "Skru ned lyden", which is more common in Norwegian.
Is volumet also used for shapes? (E.G. The volume of a cylinder is the area of the circle at the base, multiplied by the height.)
Yes, though that meaning wouldn't be an option with the verb choice in this sentence.