Visit the Sony Creative Software website and I'm sure someone will be able too answer your question on they forums. My guess would be that it should work with Windows 8; to be sure you can always download the demo and try it on your computer first to be sure.
It should; make sure of to install the correct bit platform. The Movie Studio Platform suite come in 32-bit and 64-bit so check your Windows 8 system type to take the full advantage (I think the Movie Studio installation process will determine the system type of your Windows 8).
It should. The Movie Studio software come in 2 system types (32-bit and 64-bit). I believe the installation process would verify your Windows 8 system type and let you know if it is compatible or not (so that you do not install the wrong system type version).