I get this game recently and figured if game was too slow I could use this mode to speed it up but when I press f11 while in the game it doesn't do anything? Not sure what to do, any helpful hints would be nice- other than that no errors or problems just can't get it to start when i press f11.

There are 2 shortcuts for the game, one to the normal version, and the other the Developer Mode version with the cheat window enabled (this version has a red text warning on the left side of the main menu screen).
IIRC the GOG installer just puts a shortcut for the normal version on the desktop, the other should be in the start menu folder for the game. You can also start it directly from the install folder, or create your own shortcut (..\Divinity II - Developers Cut\Bin folder - Divinity2.exe is the normal mode, Divinity2-Debug.exe has the Developer Mode enabled).

No, it should work in a new or existing game, and you should be able to load a save in either version or start in one and switch to the other.

Are you playing on a laptop, or something, that could be doing something non-standard with your function keys?

On a desktop with microsoft keyboard but it is wireless- I'll try a wired keyboard see if it makes a difference

It was the f lock button for the f keys