Hi Josh,
The black part is the pressure pin that pokes out of the bottom of the handle and locates in the base when the pot is secure for roasting. The flatter top locates the spring so the pin is sprung loaded. I think these images will help explain what I mean.



As for the screw in you spare items!, I'm not sure where it goes. If it came out of the pot assembly then it might be one that holds the metal base to the bottom pot frame or the lid spring, but that should be obvious as there will be 3 screws and a spare hole

Or the spring clip in the lid will have been in amongst the spare parts!

If none of those, then it must be from inside the handle, possibly holding some retainer for the sprung loaded pin. I've not taken mine apart, so I don't know exactly what is in the handle cavity.
Hope this helps.
Cheers
Mr A