Hi Lonnie, what a great project for your school. Take time to be amazed at some of the near century old technology, the vision the ol' Dodge Boys had with this car!
Ok I'm gonna tackle the easiest part of your post. The needle valve cap is removable pretty much for just one purpose. The top of the needle shaft has a slit in it, solely for the purpose of putting a screwdriver blade in it to turn it on the pretense to shift it for better seating. That's it. So yours is missing - only harm is a source of dirt (marginal) IMO. Mebbe you could find a cap nut to fit at your local hdwe store. Or even a plastic cap.
On your needle valve, dunno your source for parts, I recommend asking Tom Myers, Myers Early Dodge
www.myersearlydodge.com to be sure you have the right part for the right Stewart carb.