Electrical installation - is everything okay with it?

Oh yes: The installation is not professional. There are unused wires hanging loose, which is not allowed. They must either be routed to terminal blocks or to Wago connectors. However, the Wago connectors must not be lying around loose - this is not permitted in a distribution box. That would be the second unprofessional aspect visible in the photo.

Furthermore:

- Electrical equipment must be arranged so that their operational use, inspection, maintenance, testing, and access to the disconnectable connections are easily possible.
- All electrical equipment must be accessible for testing.
- The assignment of the conductors introduced from the outside to their circuits must be clearly and permanently identifiable.

I would say the main problem is the distribution cabinet being too small.

Well, nice is something else. WAGO terminals actually have no place in the distribution box.

According to WAGO, they are allowed there with the appropriate WAGO mounting adapter; but of course not like in the picture.

The two exposed wires are somewhat to be criticized (but you see that more often than you think (of course only if they are not connected on the other side)).

“It is recommended to provide additional conductors for maintenance. If spare conductors are provided, they must be connected to spare terminals or separated in such a way that contact with live parts is prevented.”

In our electrical box we have three fuses, of which I had to replace one now and then (there were two 10 A fuses, which were replaced by 16 A fuses, and one 16 A fuse). Last weekend for the first time a 16 A fuse “blew”, so nothing worked at all… unfortunately I don’t know when it happened, since we only noticed it in the morning while showering because there was no hot water since the heat pump also had no power.

But here you are speaking in riddles. First, they are not visible in the picture, and secondly, it is not clear who increased the fuses (arbitrarily?) from 10A to 16A. Also, what is the purpose of these fuses?

Do you still have a 3-pole circuit breaker (with 63A or similar) in the distribution? Or only these fuses?

Also, how many RCD circuits are present?

The more often you look at the photo, the more errors you will find:

On your circuit breakers, there are partially three wires connected to the output. A maximum of two is allowed.

Hello, the electrician said he accidentally screwed in two 10A fuses, I should just use 16A. As a layman, I don't really know the purpose of the fuses, I only know that if one is out, neither my heat pump nor my major electrical appliances work... As far as I know, an FI is present. However, I will take another photo of the entire box this evening, maybe that will help. Is there any way to have someone independent take another look or do you think that would make sense? Measurements were carried out on Saturday, the colleague said that according to the measurements everything was fine.

the electrician said he had accidentally screwed in two 10A fuses, I should simply use 16A.,

No, he should come and fix his work properly.

That is already a violation if he asks you to replace 10A with 16A. You are not an electrical specialist. What if the wiring is not designed for the current load?

Apparently, there are some serious issues here, and if I were you, I would insist on a 100% standard-compliant execution.