Just to clarify, is this the processor fan or the case fan?
Also make sure you are not confusing the noise with a HDD spinning up, which would happen when you start programs, etc.
Maybe I'm just being really paranoid, but if I'm buying a used card I always assume it's been mined on.
Even if the seller explicitly says they didn't, I just assume they are lying. I figure that's the safest approach.
I agree, there are a couple areas AMD needs to improve in its graphics cards before it can seriously compete with nvidia. Like making better freesync, or a card to compete with the 1080ti (and soon the Series 11)