House Purchase - Complicated Situation

Your concern is very personal, so some answers might also land with you more emotionally. One or two questions that I consider important unfortunately remain unanswered by you so far; ultimately, it’s none of my business either.
It can happen that at some point you get tunnel vision and no longer really see the position of others.
Such a proposed solution can only work if really EVERYONE!! sees a "gain" for themselves, but clearly the first problems are already emerging. As I said: €100 is quickly divided, €100,000 not so easy.
Everyone wants the biggest bite possible, and I would not exclude myself from that either.
The problems or rather the mistrust are already affecting the relationships, as you can see. So – everything is completely "normal" with you guys :D
Maybe it shows you that you can also become quite unhappy with such a house purchase.

Unfortunately, I don’t think we can amicably agree on a market value.

...which would settle the thing. Why do you children check the value of the house and not the parents themselves?

The move to a 1-2 room apartment

The focus should be on "nice," "special" for Dad, but here it is rather left to chance "preferably nearby." That sounds too casual to me...

What to make of that is another matter .... ?

The other children simply want an advantage just like you, even if their reasoning is exaggerated. I find your approach understandable but also quite one-sided.

and that he won’t constantly "interfere" with us.

...not constantly? ...but sometimes, when HE deems it necessary. Such unclearly regulated things make my ears ring... Either it belongs to you completely or not at all. That’s why I pay my things properly or simply don’t buy them. There seem to be many mutual, unresolved expectations here... As long as it’s cheap.

Therefore, in my opinion, it is all the more important to obtain an expert appraisal/opinion of a third party about the house value.

That won’t calm tempers. Either it’s too expensive for you or too cheap for the others... and Dad ends up in the micro-apartment.

The wish comes from both us and my father.

...and why doesn’t he pursue his own wish with a notary instead of the children calculating up and down? It belongs to him after all.

The move to a 1-2 room apartment (preferably also in the immediate vicinity) is perfectly okay for him.

"Okay" is the little sister of crappy (sorry). Why should such a homeowner (father) live fairly mediocre at most in the future? In old age he will be living IN the apartment rather, so it has to be nice and comfortable for him there, with suitable size, location and equipment. That gets lost here! And... still no answer on care/support!!!
"Preferably also nearby" does not sound like a reliable arrangement for the father to experience security and comfort in old age from those who were favored before. Advantage is great but then please reciprocally.

There is also a mother (living in a rented apartment), they are separated.

Now I am shocked!
Apparently it does not belong to the father alone. What does the mother want then? She lives renting? Is she also asked? How is she secured? Does she also want to give away large parts of her own security during her lifetime without compensation? Why don’t father and mother clarify that first?

That means everyone would get half from the potential house sale, which should at least still be enough for a generous down payment on my father’s apartment.

So dad can only make a "generous" down payment on his condominium because children want to pay. The mother lives renting... and all children will then live in their own houses??? Wow!
For me, as part of the older generation by now, something is wrong in the order here. The parents live in small (rented) apartments and are ultimately probably away from the children. How can you already want to divide the parents’ inheritance now, when both are still alive and apparently not well secured?

It would only be problematic if the house is really appraised at a very high amount.

Problematic for whom? That would simply be correct!
To me it says that then Dad and Mom don’t have to worry in old age. In my environment, such a dad regularly sat on the terrace and cried because he never imagined it that way.
I do not want to attack you personally, please don’t misunderstand, but rather motivate you to leave your own tunnel vision. It’s enough if the millionaire brother is already in there.
I find the idea completely inappropriate given the known situation here, because the two parents must first be cared for, including in secure living arrangements, before the youth sharpens their knives. But I do not read much about that here.

I have not yet understood from the answer why it is important to the father that the house stays in the family. It should be irrelevant to him in his new apartment – so why isn’t it? – this motive should be examined. If the father still has a long and happy life after his move instead of passing on the house on his deathbed, then his children should all be happy for him rather than envying each other over who makes more of his talents than the other (I am definitely too little biblically literate to say where it says that – but it is indeed in this very old book, so it is not a "new" problem unique to your family). With siblings like these, I would call the dogcatcher to take them to the orphanage. Seriously, troublesome relatives, even as a gift they are too expensive. The dreamer of appreciation should get the house and pay out the other siblings based on the fictional million – bet he wouldn’t mean it like that then?

As siblings, I would feel pretty fooled.

No envy at all. Don't you grant that to your brother or sister??
If you share it, either everyone has to move into the house, which probably causes space problems, or the house is sold and everyone is paid out.
However, I would not sell my parental home. Memories and home are surely worth more than a bit of paper.
The siblings can always come over for coffee, and besides, with some sibling love, you will surely come to an agreement.

No envy. Don’t you grant that to your brother or sister??

What I mainly meant was: doesn’t the brother deny the father that his moving company is not immediately the Grim Reaper? – because basically the "luxury problem" logically arises only through the time between moving out and inheritance, in which an increase in value can actually occur. Some people, when they sense a chance to envy, have such a cold heart that they don’t even realize to turn on their brain before thinking. If I were a pastor, the next sentence would have to be: "they must have our special intercession" ;-)

Perhaps this one? "Whoever troubles his own household will inherit the wind, and the fool will be servant to the wise!" Proverbs 11:29

No need to be jealous. Don't you grant that to your brother or sister??

If that's how it is with you, I sincerely congratulate you! It doesn't have to be a matter of contemptible envy. Imagine your parents give you €50 at Christmas and your brother next to you gets €100. It's not about the small financial difference; if you feel uncomfortable about it, money is in the background. It would feel the same with €90 and €100.
As a father, I would ask myself why I favor one of my children? Especially THAT is what I do NOT want, not only in the financial area.

The siblings can always come over for coffee and otherwise you can surely agree on something with a bit of sibling love.

Father stays living in the house and the brother gets €100,000 more from the father and the sister may then be happy when she sometimes gets to ride as a passenger in his new Porsche. That should be what "sibling love" can allow, right?

I mainly meant: doesn't the brother deny the father that his moving company is not first the Grim Reaper?

Exactly! Again and again I read about such constructs and that the inheritance is planned during the lifetime if it suits the favorites and the "old ones" are simply forgotten or somehow only considered casually. You can even look up the meaning of the word "inheritance" on Wikipedia; they all have smartphones after all.
There is also the very simple and obvious possibility that all siblings come together and enable the father to remain in his own house (which HE is so attached to) through their support. The house is too big for him? Great. Each of the children sets up their own room there and visits dad frequently, even better for the grandchildren. Grandpa sits in the garden chair and enjoys the sight of his offspring who are just maintaining the garden or playing in his well-kept garden and can stay overnight there anytime.
I know that this old-fashioned stuff sounds strange to some, but for me it actually means lived family and social behavior within the family.