This works as intended as if you stand on a wall, it will put you a half block up too since the player and the primed TNT are entities. The half block is what the game does to prevent you from jumping over fences and walls.
If you're talking about enchanting it again with the enchantment table, WAI. A simple wiki search will confirm that.
This works as intended, this is what entity render distance is.
Just figured out that it probably has something to do with the fact that this is a school network
Szymon, this is not a bug that you should be concerned about unless you are purposefully trying to fall through the world. It is a problem with the very way the game stores the position of entities, and furthermore should not prevent you from playing the game until you are planning on an expedition that requires you to walk in one direction for 30k blocks or more. To fix this bug would either require a fixed hitbox like mentioned above, or a rewrite of how the game handles an entity's position.