You can rewrite the drone to category C1. This is done via the Dji Fly app. This means that the altitude restriction is no longer from the take-off site but adapted to the terrain (or can be set to max. 500m) and you can also use the Battery Plus, as the drone no longer has to weigh less than 250gr. In contrast, you have to obtain a drone licence (possible online from various suppliers) and you have to provide the drone with an ID sticker... I did this with mine and it was no problem.
Yes, the 120m altitude limit applies from the take-off point. You can request an increase to 500m from DJI (via the app or website), but then the C0 classification of the drone is cancelled and can no longer be reversed.