You don't need to pay any fees to YoYo Games.
However, if you plan on exporting to Mac, I'm pretty sure you need to pay Apple for a developer's license. I forget how it works. But if I remember correctly, GameMaker doesn't even let you export to *.app if you don't have the Apple developer's license. (The developer's license is subscription-based. I think one or two hundred dollars for a year, and then you need to pay again each year when it expires. Kind of a ripoff, but I did it last year because I needed to export an early prototype of my game for a school assignment
Now my Apple license is expired so I'll need to pay again once I get around to finishing the game.) Additionally, if you plan to export to Mac *.app then you'll need a Mac.
As for other platforms, I don't know. (Never tried exporting to Windows or to anything else.)