I'm not sure where to post this only because I have both mac and windows on the same system. I've just upgraded my hard drive in order to increase my space and it's asking me to purchase another key...
You can only use Parallels Desktop on one OS in a device, not with two. The key you have purchased is primarily for Parallels Toolbox - Windows.
Yes, you can. If you are facing any issues, let us know to assist you further in resolving the issue.