What is this? Windows start on 2nd floor. So in the example below, we have 0 floors and 1 window, meaning we need to increase the amount of floors by 2.

[TestCase("w", "Bob: Reduce the amount of windows by 1 or increase the amount of floors by 1.")]

Can we rely on Environment.NewLine? Shouldn't we specify \n or \r\n in the description and in code?

A trailing newline is expected but was not mentioned at all.

Every random test expects the same 20 floor house with 20 windows and a door.

This seems to be a problem with codewars at the moment, as every Kata I try has this problem currently.

When I'm doing the test, I systematically get an "Unauthorized" message.
I'm new, and I don't understand why?

You are right. Here are benchmark results

Counting elements in a collection is a duplicate.

This is incredibly slow, as Enumerable.Range needs to generate every number in every range you feed it.

Maybe ensure that the elements in notes are in descending order. Something like |> List.sortDescending in the assignment should convey that the elements cannot be in random order.

This code is not f# idiomatic. I recommend reading fsharpforfunandprofit. It is a great read and improved improved my functional programming tremendously.
https://fsharpforfunandprofit.com/posts/thinking-functionally-intro/

I upvoted this solution for being clever, but it would almost certainly fail with very large intervals.
For example consider: (0, int.MaxValue). The length of this example interval is over 2.1 billion -- LINQ uses an in-memory Set<int> to track the 2+ billion unique integers coming out of Distinct(), followed up by the counting of 2+ billion unique integers -- either a timeout or OutOfMemoryException seems likely.

MS Reference Source for Distinct()/DistinctIterator(), see also: source for Enumerable.cs on GitHub; search for Distinct

The current "random" test isn't random at all, it's just enumerating the input range of ([50-60],[50-60]).