Kayla -thank you for offering to help! The nuts have the same thread as a bottle cage bolt – so M5, I’m guessing. The extended top hat on the C*1 nut in the pic above is there to fit into the recess in the shifter bracket and hold everything in place, a bit like the nut on a chainring bolt is used to align the chainring with the hole on the crank’s spider. The bolt doesn’t protrude more than about a millimeter past the hole in the shifter bracket. Not sure if I’ve explained that terribly clearly – so apologies in advance.
Here’s a pic. The green bolt is a standard disc rotor or bottle cage bolt, with the shifter bolt from the drawings above on the right and a chainring top hat nut on the left. Even if you could give a name to the top hat bolt, that would be awesome!