Notating Illegal Moves
I think that a simple "illegal move" comment would suffice.
I don't think you can go back and protest the result, even if it is on tape.
I'm not aware of any special annotation for illegal moves. One thing to keep in mind is that some chess GUI programs won't allow illegal moves to be entered. Sometimes there will be a setting that can be changed regarding "check move legality" (or some similar phrasing). Disabling the setting would allow illegal moves to be made in the GUI.