The "headset cap" or "conical spacer" or "bearing cover" is needed to protect the bearing from dirt and water and sweat and such.
The stem can sit directly on top of it in almost all cases.
There should be nothing above the stem besides the top cap for the compression plug. In some cases a 5mm spacer above the stem is used, but that's the max allowed unless you're using a special compression plug.
A forum community dedicated to Road Bike owners and enthusiasts. Come join the discussion about bike parts, components, deals, performance, modifications, classifieds, troubleshooting, maintenance, and more!