Strom-Cloud experiences vs. feed-in tariff?

With about 81m2 of usable roof area, the photovoltaic system would have a rated output of 10.56 kWp Storage: 10 kWh (4x 2.5 kWh lithium-ion batteries with integrated inverter)

Incredibly expensive. Sounds like a defensive offer.

I have now taken a little look at online calculators and, based on the data of the pure photovoltaic system, I would have a net profit from the feed-in tariff of around 250€... Would that be realistic? Photovoltaic system annual yield: approx. 9000 kWh Self-consumption: approx. 6500 kWh (3000 kWh electricity consumption / 3500 kWh heat pump) Feed-in tariff: 10 cents

Without being able to confirm that, this refers to the system above at that price? It should not cost more than around 15K € gross without storage. You should never do that at the mentioned price.

I have now calculated with the nominal power of the mentioned photovoltaic system, which can certainly be obtained at a much cheaper price, right? Or is a 10kWp photovoltaic system oversized for my annual consumption of about 6500kWh???

In principle, as much as possible applies. If no more than about 13 kWp is possible, then no more than 9.9 because of the Erneuerbare-Energien-Gesetz-Umlage. But as mentioned, the motto is: go big or go home!

As says, the fuller the better. The corridor he specifies is also correct. But I believe no persuasion is necessary, since still assumes personal use.