that sounds like a mouse driver issue? i dont know, i have never seen that happen in my projects.
try this: delete config.ini, game.exe, openal32.dll, startup.log in your projects folder. open efpse, open your game, then test game. it will remake all those files you just deleted. does that change anything at all?
also try this: use build and pack and make your game. move that folder, then use build without packing. test both versions of the game. do they behave the same way as the testing in the editor? i know i was unable to use build and pack when i built my last project for the game jam, the game.exe ctd'd after loading the first map. but using build without packing it worked fine for me.
if all three versions of game.exe are doing the weird mouse movement thing and not remembering your fullscreen settings then....... i have no idea.
people have been ducking and dodging around crazy bugs like this for years with RGM, so as a community i think we can figure out how to work with this engine in it's current state until the world becomes a better place and jessicochan can get back to dev it more.