Install photovoltaic power storage yes or no?

No, these are all net figures, meaning usable capacity. There are 10.2 kWh usable.

It is December, so it is dark not only at night. Sunset is shortly after 4 p.m. and sunrise is not until late in the morning. This is also household electricity, for example cooking dinner, baking rolls in the oven, TV or whatever else happens in the evening. But yes, the heat pump also draws a lot. I have set a hot water block from 10 p.m. to 10 a.m., but the heating often runs at night as well when it's below freezing.

Warm water cut-off set from 22-10

Until 10:00 in the morning? But are there still leftovers then or can you only shower cold beforehand?

What should happen to all the warm water overnight? People shower in the morning, after that it might be cold. So far, no one has complained about cold showers.

10 o'clock simply has the background that currently no sun shines before that, so I might as well do without the lock. And since we both work or the children are at school, it doesn't matter at all whether there is warm water at 9 o'clock or 11 o'clock.

Hi,
so about €600 savings per year, about €6000 over 10 years.
What does the storage cost in return?
Is it worth it?
Olli

My calculations have so far always shown that a power storage system is currently still not really profitable.
There are too many factors that have to be favorable for the storage to be worthwhile; in reality, you are more likely to incur losses.

Furthermore, electric cars will increasingly hit the road in the coming years. I am sure that this multi-billion market will bring not only new, cheaper, and more efficient battery systems for cars but also for homes.
Therefore, I would definitely wait for now.

Car and home storage are only conditionally related. It is even more the case that the demand profiles differ significantly with regard to weight, fast charging capability, maximum power output, and continuous power output. Such a motor with 100 kW draws completely different currents than a household. This also results in completely different ideal chemistries for the battery. Currently, the use of Li-Ion in the home is rather a makeshift solution because there are few market-ready alternatives. If batteries for the home become cheaper, it will be more because they are developed differently than for cars, not because car batteries are produced more cheaply.

Sure, that's true, but according to the internet, for batteries of electric cars

According to a graphic from the news site, the average price for a kWh in 2010 was still 1,160 US dollars (currently 1,040 euros). Last year, 2018, it was only 176 dollars or just under 160 euros

With these prices, I would also install an inefficient battery for the house, it's still many times cheaper.
And as you yourself wrote, currently there are few market-ready alternatives. This will certainly change in the next few years, and a present-day battery can hardly be so profitable that installing it now pays off.
(Exceptions prove the rule)