"A term often used in the verse, with various meanings. While world usually refers to a universe, there are certain times when it also refers to a planet, though this is rare. The Author of Maou Gakuin usually uses the word Earth to refer to a planet, and thus it's completely safe to assume that world means universe in the various different statements, unless specifically stated to be otherwise or contradicted by other statements." - Since this part doesn't have any evidence behind it and is only a claim, there isn't really much to debunk. However, I can say that this is wrong and is just your headcanon.
"Above the sky and below the earth, a black dome stretches out. What was added around the world drawn on the blackboard was a black sky, a black dome." - The sky and the earth together is acknowledged as the world. If the earth itself refers to the world, then instead of saying, "What was added around the world. . ." it would've said, "What was added around the world and the sky. . .". Therefore, the use of earth just refers to the ground. Another thing, this black sky that is infinite in size is described as "added around the world" not "part of the world'.
'The farther you go from this earth, the more the black dome is stretched and the closer you get to nothingness. It is here, in this near-infinite sky, that the divine world is located. A 'Blue Dome of the Gods' is added to the black dome.' - Just as the black sky isn't part of the world itself, the Blue Dome of the Gods that is part of the black sky isn't part of it either. Which means we have three separate spaces: the world itself, the Blue Dome of the Gods, and the black sky. Since neither the Blue Dome of the Gods or the black sky are a part of the world but reside in the same bubble, we can conclude that they can be considered the rest of the universe. If this is the case, then the world is simply what one would normally think of when the term world is used, AKA the planet. It's not uncommon whatsoever for world to be used instead of planet in various forms of media.
"'This is what we call the countless dark bubbles floating in the Silver Sea. It is said that all worlds begin with bubbles. Even the deeper worlds, located in the depths of this ocean, was one bubble in the beginning." - "It is said that all worlds begin with bubbles". Look closely at that statement. All worlds begin with bubbles, not all worlds are bubbles. Sure, bubbles can also be referred to as worlds, but worlds can refer to the planet as well. In this case, it's quite clear that it refers to the planet. If not, then it'd be saying something entirely redundant like, "It is said that all bubbles begin with bubbles." They can clearly be different things. World has never once referred to universe. World has either referred to the planet, or the bubble which qualifies as a universe. This being the case, it eliminates the possibility that world referred to universe instead of the planet in this scenario. As the author has also used the term universe itself, it's clear that he doesn't use world to refer to universe.
There are many layers in the Silver Sea, and there are countless bubbles in each layer, and there is an infinite sky in each bubble. There, it stretches on endlessly with no end, and it is where that world's God is located. Each god has its own world, and there is a deeper world, the world of the Lord God or the abyssal world. - After this part, "There are many layers in the Silver Sea, and there are countless bubbles in each layer, and there is an infinite sky in each bubble." everything referred to is something within the bubble. With that cleared out of the way, it'll be easier to explain. "There, it stretches on endlessly with no end, and it is where that world's God is located.", this would be referring to the Blue Dome of the Gods. So seeing this statement afterward, "Each god has its own world, and there is a deeper world, the world of the Lord God or the abyssal world", since everything mentioned is within the bubble, the "Each god has its own world. . ." refers to the planet that all the races aside from the divine race reside on while "there is a deeper world, the world of the Lord God or the abyssal world" refers to the Blue Dome of the Gods, as that is where all/most of the Gods normally reside. So, once more, if the "deeper world, the world of the Lord God. . ." obviously refers to the Blue Dome of the Gods, then the regular world is just the planet.