Ah the compression cap.
Tightening this will press everything together as far as the upper
and lower headset bearings. Don't tighten too much as to not allow
bars to spin freely, but don't have it loose so that there is wobble or
play in the forks/bars. After tightening the compression cap, then
you tighten on the stem. The compression cap is no longer needed
at this point. You could take it off once you tighten the stem, but you
might as well leave it on, incase your stem bolts come loose some day
then your compression won't be affected.
Basically, it's purpose is to press everything together
so you can tighten on the stem without having to squeeze it all
together yourself.
Could it be your headset is wrong or broken? Check it out.
Your handlebar has a built in stem, so the stem and handlebar are one.
I would grease the bolts on your stem, but never the fork's steer tube.
So here's the deal, you tighten the compression cap so that everything is
held and the bearings in the headset are seated nicely.
Now you can ride without wobble but your bars will turn without your fork
or vice verssa; so you need to tighten the stem/bars bolts. That'll make it
so they don't spin independent of eachother but function as one.