Theres this glitch with my world ground height where in ZeroEditor it doesn`t show the same height as in game. For example, in ZeroEditor the ground height could be at 0, but in game it looks like more or less.

The height? The height should be fine. Make sure you look as close as possible to your props/objects when placing, moving or rotating them in ZE.
Did you resize the terrain? Make sure you use numbers like 128², 256², 512², 1024²...numbers like 100², 500²...won't work very well and causes the terrain to move to complete different position.