shortcuts can override normal keyboard input

This also works with some other keys like "enter" or "."

I guess shortcuts should always require a modifier key, e.g. shift, ctrl, and super, as I can't think of any exception.

If you always require a modifier, extra keys on gaming keyboards will not be able to be used as efficiently.

I don't really think you can do it simply by disabling keys without telling the user what is going on. For example I just tried to set shortcut for screenshot to PrtSc button which is disabled - I had no idea why every time I pressed PrtSc "Disabled" appeared. But then I noticed that Ctrl+Print worked so I said to myself: "Aha! Let's make a bug report!".

1) Let the user set any key to anything they want and provide them with a option to reset given key to its default value so if the user sets space to anything else than space then they can just go to keyboard settings and reset the space key to its default value. If you'd like to go bulletproof add reset to default button to every command as well. Also a way to reset all keys/commands at once would be a useful feature.
2) If you think that it's a good idea to disable certain keys, make it tell the user that the key they've pressed is disabled and that it's not a good idea to use it (make it feel like a feature rather than a bug) but give them an option (checkbox or anything) to use it anyway because people use many odd shortcuts (especially in the Custom section!) and they're not happy if you force them to change their habits.