No, you are not allowed to simply level your property as you please – with or without neighbors. You need permission from the responsible building authority.
Yes and no. In most development areas with a zoning plan, there is a specification in the range of 50cm or 1m, so that within this tolerance you may raise/lower/level the property without an additional/explicit application. However, always only in total – local fill or excavation is considered as individual components.
The planned heights are shown in the building application and then it is okay.
If no specification is found in the zoning plan, the respective state building code applies, i.e. always the next higher legal source.
Best regards
Dirk Grafe