How important is it to completely even out the part when sanding? I have a stubborn part that has a hard time leveling out, and after multiple sands and epoxy layers, it's not sticking well and letting me sand it level. Will adding clear coat cover this? or will it show through?

Looking at it head on will probably look fine, but depending on how deep they are, when you look across the surface you'll see them

Your part is very similar to mine and I had a pig of a job sanding it smooth. Just don't be stupid like me and try using 120 grit, you'll never get the scratches out!

Check out this thread, some good advice here.
http://www.talkcomposites.com/11473/Getting-a-good-finish-on-a-plug?PageIndex=1

I'm really only a learner here myself but I wouldn't use anything rougher than 400 before going on to 800, 1200, 1500, 2000, 2500 and cutting compound.

Maybe someone more experienced might be able to advise better.

Use the highest grit that can do the job. 

Don't bother sanding it down smooth if your going to clear coat.

Fill the low spots with APF7 its a black filler for carbon then 800 and clearcoat you will never see the spots of filler

Don't bother with the smoother grades of paper its a waste of time if your clearcoating,not if your polishing the carbon thou

I've had things like this in the past.  They do fill with lacquer and it looks OK but you do get a ripple in certain lights.  If you ladle on the laquer and then flat it back you can get it properly smooth.  I go down to about 360 and then recoat the lacquer.  Anything smoother than 360 is wasting your time IMO.