When i install the patches, it creates a new folder in Program Files (x86). Should I instead install them to the Empires folder in GOG Games?

I installed them into the Empires folder under GOG. Also, I wanted to add that i renamed the movie files under Movies folder and changed my display scaling option to 100%. That fixed the black screen issue on Windows 10 and the game runs perfectly.

What patches did you install?
Is EDotMW not already patched to the latest version?

That happens for many games. But as far as i know, GOG\Steam release have all content and latest updates. But probably im wrong cause this is not original publisher, but "steel-*somewho*" and Rebellion. So they can bring broken update or miss content origiallly published by Activision.