The ping lag is solely because of your own connection pate, or from the servers you play on being laggy for some reason. I've never had lag problems unless the host sucked, in that case he often gets replaced quickly. I play on Xbox Live though, experiences may differ with PC / PS3, not sure what you're playing, I'm assuming PS3 if my memory serves me well.
As far as I know there's no special op missions you need to co-op on? What are those missions called? I'm pretty sure I've done them all both alone and in co-op mode unless my memory is failing me. Sadly I can't log on to check as my Xbox got the RRoD (red ring of death) yesterday, I'm so pissed off. Going to buy a new one later today.
As for the game, it rocks, and I'm still playing it pretty much daily for ~2 hours. I never play alone though. I just don't find games like this fun to play with random dudes, it's a type of game I need to play with friends for it to be fun. Unlike MMO's that I can play for endless hours all by myself, I get bored of playing MW2 after just a few rounds online if I play alone. Just bought the Resurgence Park a few days ago, man it rocks. The new maps "Fuel" and "Carnival" are totally awesome. "Vacant" and "Strike?" weren't among my favorites from MW1 really, so I'm a little dissapointed that they included those. I would have preferred other maps. "Crash" was my absolute favorite in MW1 though, so I was really glad when it was included in the Stimulus package.