All wastewater pipes in the floor slab are incorrect.

. I will now involve a lawyer,

What do you want a lawyer for in the early stages? That's just child’s play, sorry.

Get yourself an expert construction supervisor as soon as possible. But you have to check whether he is even allowed on the construction site.
He decides whether there needs to be a dismantling or whatever.
And if you are supposed to make a progress payment after a construction phase, he has to approve it. Otherwise, the general contractor or main contractor gets no money. No idea how it works with property developers.

That’s how it went with us, and even in the basement they first discovered too little reinforcement steel and inadequate waterproofing which were promptly fixed.
We paid him 3500 euros for supervision during the construction period and it was worth it.
He had several projects to supervise and regularly came to the construction site with the documents.

The construction manager did react immediately and came on Monday... but his statements made us suspicious... that would not be a problem... they will be filled with concrete and we will do core drillings???

If done properly, that is a good solution without compromises for you.

Now our question: is it possible to properly install all the pipes afterwards? What solution must we accept? Can we insist on a new slab?

Yes, that can be done properly. The solution is good, there is nothing to "accept". Of course, there is no reason to insist on a new slab. After all, no damage has occurred.

Trust is already very shaken, moreover they delivered us facing bricks that look as if they were painted with nail polish and well... partly already chipped, so the red tone is visible (our house is supposed to be dark faced) - his argument... you don’t see that on the wall, they don’t absorb that much water :( our house will cost about €300,000... I am sad that we have been fobbed off like this so far...

If you are unsure and nervous, get help from an expert as already suggested, who translates the statements of your construction manager to you and helps to intervene if it is really necessary.

I will now involve a lawyer, -thank God- we had secured ourselves beforehand. Let’s see what they say... we are thinking about whether we even want to continue building with them... And about the facing bricks – we were presented nice panels at the sampling appointment where not a word was said about the condition... if I had known that they only contain color superficially, I would never have chosen them

Settle the matter with the damaged facing bricks (defective ones must not be installed) and learn from it to deal more with the material yourself or select things when you have someone with expertise with you. That the facing bricks are not fully colored is not a defect.

What do you want a lawyer for at the beginning phase? That’s kindergarten, sorry.

There is no need for a lawyer. Although the behavior does not remind me of kindergarten, it reminds me of a "fear-biting dog" that reacts to its own insecurity with rejection and aggression towards others. With this behavior, you create more problems than you solve – and some problems you see now may turn out not to be problems at all.

The shell constructors simply rotated the house by 90 degrees and accordingly excavated the strip foundations. The expert did not notice,

Apparently, the culture that "garden" is at the top instead of "north" in floor plans has even reached experts ;-)
The lack of rotational security is probably the most compelling argument against square floor plans *LOL* – I can’t believe I hadn’t thought of that before...!

If I had known that they only contained color on the surface, I would never have chosen them

It seems to me that the widespread general citizen’s right to lack of education is now getting out of hand: just as there are no pale purple cows in nature, there are also no occurrences of aubergine-colored tones! – you’d have to come to the conclusion yourself to ask whether the material is dyed through or just surface colored. That it is colored must surely be clear. Fish don’t grow as sticks – seriously, why is there even a show called “The Mouse”?