Why doesn't Lan multiplayer work if we put mods in call of duty modern warfare 4?
Because there are no game legal mods and it is just a form of cheating
Unfortunately no, you can't play multiplayer on Call of Duty Modern Warfare 1 or on Call of Duty Modern Warfare 2 on the same screen. But on Call of Duty Modern Warfare 3 and Call of Duty Modern Warfare Black Ops you can play multiplayer on the same screen. There is an new Call of Duty Black Ops 2 coming out soon though, so I expect that to also have that feature, since its newer.
I would say that Call of Duty: Modern Warfare 2 is better, because of the weapon selection, perk selection, graphics, gameplay - both multiplayer and singleplayer storyline, the killstreak reward selection, the offline multiplayer class customization feature, and the online multiplayer gameplay. Everything about Modern Warfare 2 is better. Except the price.