dmg is a disk image. It can be mounted onto the desktop & appear in the same way as any disk does.
.dmg - Wikipedia, the free encyclopedia
No the windows version is different. It is an exe file which does not open on any other computer platform other than windows. So you will need to get another copy of pro. Else use Basic.
Your Pro support will have finished now as last year they were only offering support & free updates for 6 months. Not until very recently did they introduce the option to get Pro support for 12 months. At the end of the period your name is automatically removed from their database. During the last 4 weeks of support they offer a discount to continue with support. This can be seen on your personal download page during that period. That's why I always recommend to all pro users to BOOKMARK their personal download page & check it periodically.