As the question says.
Yes.
Most PS3 games have dedicated servers unlike 360 game which use P2P.
You connect to Sony’s servers and they connect you to everyone else.
But I guess you knew how ti works.
One to host a game.
Around $30~$70 would be nice.
List as much as possible please.
Your best bet is to look for managed dedicated game server hosting on google or yahoo, swear to god that you will find at least 30 of them!
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In order to play most PC FPS games, you need to connect to a server. All players talk to the server and the server talks back to all the players. Basically, the server is the "room" everyone is playing in. A DEDICATED server is a server that is ran using a separate program that ONLY hosts a server. Even if there are no users playing, the server will remain online. A listen server is started from within a game. When the hosting player leaves, the server closes.
I’ve been playing modern warfare 1 for a while and was gonna get this game for my birthday but I learned that they didn’t have dedicated servers when it first came out. Do they have them yet, because I hate it when you can’t kick cheaters and you either have to wait em out or find a new server, thanks.
Short answer- No and they dont look as if there will be.
What is this protest that everyone is signing and is it only on the PC?
Oh and I don’t have it on PC so I don’t know what the dedicated server is and why is it bad not to have one?
Well if you played the first one you should have noticed that maybe one or two servers you go on are always there. Those are dedicated, when its not dedicated people will have to start they’re own servers for you to play.
I don’t even play it on the PC but I’m curious. Apparently it’s going to be ran on a "player-to-player matchmaking system" rather than dedicated servers. I know what dedicated servers are but what would the difference be between the two for people playing the game?
the difference is that there won’t be any "this clan only" servers that are pretty important to people, along with no modded servers. 
on the other hand, people wont be able to put quake live sounds and such in their servers, which is a good thing imo. other than that there won’t be much of a difference (not that i know of).
Theres this dude in mw2 that says the guns have lack of idol sway what is that? And what is dedicated servers?
Idol Sway is when you are standing still and your weapons move realisticly side to side, up and down as if you are breathing (Because realisticly nobody can stand completely still). MW2 is not very realistic which is why most gamers prefer World At War.
A dedicated server is a server that is set up for the soul purpose of hosting a game rather than having one of the players in the game be the host. They are generally less laggy, more reliable, and less prone to hacking.