You can but it doesn't count for online multiplayer.
yes!
you can level up da
To level up in black ops you must get kills and earn experience just like anyother call of duty games.
In Black Ops, you don't get an offline multiplayer account. It only shows your playercard from your online account. So the answer to your question is; you can't level up on your Black Ops splitscreen account because you don't get splitscreen accounts in Black Ops.
straight up SD
No, you do not.
play multiplayer
Yes.
Yes, you can level up online for competitive online only. You do not get experience from Zombies.
When you rank up to level 35 you will unlock it.
Getting a lot kills
of course on multiplayer
hardcore capture the flag