I had hoped to get tips on negotiating, the question of whether such a discount is rude, regardless of my financial situation or the condition of the house. Maybe I should have left out the basics of the house, then I might have also received tips for bargaining.
I would attach a plausible explanation of why you do not want to pay the asking price to the offer.
Example: a few weeks ago we looked at my dream car, which was for sale privately. The ad stated that the vehicle was in top condition. When we did the test drive, we noticed that the air conditioning was not cooling (it was just the fluid), the front summer tires were completely worn out (really completely), and there were quite a few (although smaller) paint damages. We went there, agreed on the advertised price, but then realized that the car was not quite in top condition after all. We informed the seller of the noticed issues and jointly determined the expected costs. He then reduced the price from the purchase price, even though he had listed the car at a fixed price.
In short: as long as you can plausibly explain why the house in your view does not justify the asking price, I do not find it rude at all! It would only be rude if, for example, you wanted to exploit the seller’s distress. But you are not doing that!
So I would include a list of the investments to be made and at the end write something like “so that we offer you the amount of XY for the house, which has also been coordinated with the financing bank.”
If the buyer makes a counteroffer, consider whether you can afford it. If he refuses, then it probably is not meant to be! I would not buy a house at an inflated price by hook or by crook, which might later turn out to be a burden for the whole family.