When you Summon these Toon Monsters, it is treated as a Special Summon. This means you can do more than 1 during the same turn. However, you still have to Tribute for the Toon Monsters that are higher than Level4. But you can Tribute any monster, you do not have to Tribute a Toon Monster.
If either player's "Toon World" is destroyed, all Toons controlled by both players are destroyed. But if "Toon World" has its effectnegated, or is sent to the Graveyard, or is returned to your hand, then it was not "destroyed" so the Toon Monsters on the field are not destroyed.