Is energy storage also unprofitable for electric cars? Costs of wallbox + storage

Ah okay, that is of course a subtle but significant difference. And I would of course then need a wallbox that is photovoltaic-capable. Okay, thanks

Does the electrical supply line to the house actually need to be thicker planned for an electric car, and if so, by how much?

If you want to access the wallbox via smartphone or PC, do not forget the network cable to the wallbox.

Does the electrical supply line to the house actually need to be planned thicker for an electric car and if so, by how much?

Since we do not know what kind of connection you are getting and have ordered from the utility company, no one can answer this question for you.

5x50mm2 is already laid, with a cable length of 90m we were advised accordingly. The cable trench should never be opened again. Sauna, induction cooker and air heat pump also draw a bit and the calculated voltage drop should remain below 1%

With that, you are prepared for everything.