Who is responsible for the following defects?

So the first step is to go to the building authority to clarify whether the garage is allowed to remain there and whether you are allowed to move or build a new one at all.

Then obtain costs for the measures on the garage.

Then clarify what damages the neighbor really has on the house and who is responsible for them. From a legal point of view, the notary should be able to advise you.

Maybe an amount x can be withheld from the purchase price via the notary, from which all measures can be settled and the rest then goes to the seller.

No matter what happens, do not sign anything and do not let yourself be pressured.

He is in dispute with the current owner but we are supposed to say nothing.

You are supposed to say nothing? Then it is already clear that they are trying to push all costs onto you. Maybe they are in cahoots? Regardless, do not sign anything hastily without having clarified everything with all parties.

The new or current owner is supposed to do this according to the neighbor. He does not know that we are getting the house....
But he is in a dispute with the current owner and we are not supposed to say anything. For 20 years this was not a problem but now he wants it done because the garage of the semi-detached house is settling and pressing against his wall.

Don't get involved in any "we shouldn't say anything" story, otherwise you'll quickly be involved in the dispute and end up with a poisoned neighborhood after you move in. Just ask the neighbors (not just the one) what you need to do to become a good neighbor. Then you'll learn quite a bit.
Furthermore, as already suggested, you can clarify the property and garage situation with the building authority.
Also have it confirmed that this is the only relevant communication - it could be that the old owner was a difficult person and there are further problems.
I would not buy the house without a clear clarification of this matter.

Even if everything is clarified, contractually agreed upon, the purchase price reduced by the costs, etc. etc., the renovation of the neighboring house can still become more expensive and the cost dispute starts all over again. To my knowledge, it is rather the rule than the exception that such things end up being significantly more expensive than estimated. Once you are the owner, you have all the trouble on your hands. The previous owner is long gone, pays nothing, and feels responsible for nothing anymore, while the new owner can offload half the renovation of his entire house onto you and is even justified in doing so. Stay away.

Ever thought that the neighbor himself wants to buy and is disturbing the sale? That's why call the building authority.

He is having a dispute with the current owner [...] the notary contract is not signed

Then leave it like that and look for a house that doesn't come with a "bonus" of neighbor disputes.

So before it is exactly clarified who has to bear what or convert etc., I would not sign anything at all. Moreover, the question really arises whether one should even buy this property, as it carries a high potential for conflict. I would prefer to refrain from it unless it is otherwise an absolute dream property and a unique offer.