The Rx 200 series does support Windows 10. There is no performance difference in OpenGL, DirectX 11 and earlier, and Vulkan based games and programs between 7 and 10.
I have the exact same graphics card and Mine still isn't working with windows 10. I never got BSOD but I get non-stop screen blinking/flashing every 3 seconds. it HAS to be something related to AMD drivers but I cannot find a fix. I dual-booted to windows 10 this time, so you might want to try that, then at least you can easily go back to your previous OS. just my 2 cents. Good luck.