Yes, there is a 20 hour cooldown for repeating warzones on a character. There is nothing stopping you from completing them on a different character besides lack of people. The WZ 1 and 3 boss are harder than WZ 2 so it would be difficult to find enough people to do them a second time. That is why everyone usually goes at the same time once every day per server.
WZ 2 boss however is fairly easy and depending on your level could kill it with a small team of 5-10 players.