Can you hear your turbo spooling up? This is the first turbo-charged car I have had so I don't know if the whizzing/whistling noise is right, or not. It's quite pronounced with the roof down, and seems to get louder if the engine is under load. It hasn't changed in the last 1000 miles - so I think it might be normal.
Not a turbo expert here but not normal in my experience with turbo diesels and neither my short experience with the Copen. Do you have an air leak in any of the pipe work between the turbo and throttle body, also the blow off valve.
Typically turbo noise isn't great, a siren noise could be an air leak or the turbo on its way out. Ours is the same - sounds like a siren and then goes quiet. We definitely had an air leak and I am suspicious that there may be another. Try replacing the spring clips on the plastic inlet pipe first - this made quite a difference on ours.
So I snow fitted an alternative BOV to our Copen and the siren noise that was very promenant has now almost completely disappeared. When we first bought the car I noticed some oil staining on the plastic BOV underneath and on the point that the plastic inlet pipe connects to the metal inlet. Both must have been air leaks. I would suggest that you consider, in the first place replacing all the spring clips with a jubilee style hose clamp and then the BOV. The car drives much better too. My wife isn't overly happy about the blow off noise but the fact that the turbo is now quiet has offset that! I'll post images on my other post later today.
Which one did you get? I noticed there are some on Ebay for under £50. I don't suppose they would be compatible though.