How do I disable Shift F1 and Shift F2 to change themes?

If you are looking at Shortcuts rather than Actions, then...

Just a thought, but are you seeing this warning dialog?  If not, then make sure the field is properly active before typing the character sequence.  I find it can be easy to get this wrong so it appears not to work.  If you see a similar message to below, then you are definitely sure it will not work.

Some of the Function key/modifier options will not work as shortcuts, but will work triggering Actions.  It also differs between Windows and Mac.  F1 and all modifier combinations seem to work as shortcuts.  I was expecting F1 to be hard wired as Help.

You say you are not able to use the Fuction keys.  Are you trying to trigger Actions, or use them directly as shortcuts?