Do “Special Ops” mission level ups carry over to Multplayer mode weapons and perks

Yes. The proficiencies associated with the weapon picked up stay active while using the weapon. Your profile does not keep weapon proficiencies that you haven't unlocked if you toss the weapon or get killed.

It's the same as if you pick up a gun you haven't unlocked... Even though it's not available to you "in profile", you get to run around with it for a bit.

I can't find anyone else with this specific problem, but the general "modern warfare 3 black screen" issues people are encountering seem to be fixed by:

• Updating your graphics drivers. I think there was a special release for the BF3 beta recently that caused issues with MW3 at launch. Even if you've updated recently, check for a newer revision.
• Verify your Steam cache
• Disable the Steam overlay

Beyond that I'm afraid I don't know - there's so many tiny things that can go terribly wrong with a recent game and an individual PC setup that I'm not sure how to advise you in your current situation.

I note that you're overclocking, if you stop, does that help any? That's the first thing I try if I'm having an issue of any type while overclocking.