Splitscreen, only on console's .... and LAN ... id say Not really, because you need steam,.... i think its **** in my own opinion, but note you can do about it, you create your account as normal, unless you already have one for steam, ,... it should allow you to connect over LAN by selecting online, on the menu... that's if you have a legit version of the game, if not there is ways round it as many people know, and have proved it works, but im not going to go into that as its illegal.
However if you have a legit version of the game, and still wish to play offline, You could use :
TeknoGods_MW2SP for spec ops play, which is co-op
Read here : http://www.winmatrix.com/forums/index.php?/topic/26974-modern-warfare-2-multiplayer-servers-cracked-by-teknogods/
Due to you already having bought the game, i wouldnt see a reason you couldnt use it, aslong as you have bought the game for each individual computer.
Theres a small chance that wont work, if so let me know, and i will gladly help you out.