I don't know if this was added when they only had 3 levels, but more have been added. So, is it just Levels 1-3, then?

No, these are completely all the worlds that are in the game

So, if another world is added after the previous run is accepted; what happens to the previous run?

Well, then let there be peace with 1-3

There are now other worlds I think they mean. Like 4, 5, and 6. Also coin, sandhill, winter, vortex, spring and race world.

For the FULL ingame run it depends on what the moderators decide. It will probably stay 1 - 3 though.