Why isn't "konstnärerna" correct in this context? Is it because it is a term related only to fine arts and not music?
Yes, "konstnär" often refers to a "visual artist" like a painter or a sculptor.
Why can't the answer be 'med instrumenten' ? In other sentences it's not necessary to use the sina, but here it's marked as wrong. Is there a reason why it doesn't work here?
Why sina and not deras?
Because sina means that they use their own instruments. Deras would mean that they specifically use someone else's. Like there would be instruments of an orchestra lying around and the artits come just take them and make music
Is "MED sina instrument" idiomatic? My first thought would be "på". Though I guess that would mean they are actually sitting ON their instruments? ;o)