... spoilers for the manga ending below, in spades
When Ban was sent to live with Maria, he was actually moving from Babylon City to the GB world.
- We know it's possible to go between them, and plenty of characters have. Ban's grandma seems to have very little presence for someone with such an interest. It would be reasonable for her to have a spy, or at least to have wanted to have a spy. And he was said to be 'dead' ...
Ginji is, in reality, the God of the Unlimited Fortress
It might explain almost the whole story. Even how they managed to escape situations that were almost impossible. Also, don't enrage a God, or he might smite you. With thunders and lightnings
- Well, this is true to a certain extent. His mother was the head scientist of the project which created the universe where Mugenjou is located. And she created Ginji as a homage to her actual (and dead) son.
- Don't Forget the fact that in the Infinity Fortress, and to lesser extent elsewhere, things just seem to go how he wants without him even really trying, also in the end he becomes the LITERAL GOD of the whole GB world, of course he forgets that fact but not the life lessons he learned.