Are there any explanations or tutorials? People don't seem to discuss how they're done in the comments at all and google doesn't help either. I looked up some sheet music and pitched and adapted the horn sample to it in Audacity but 1) it takes unbearably long, 2) it does not help with the video and 3) made mistakes are difficult to correct. So what would be a better and faster way?
I can't think of a quick way to do this. It's probably going to be, as you said, an unbearably long process. I'd create the music separately from the video. That is:
First, compose some the background parts of all the songs you want to use (without the melody line). Sample the car horn. Include that sample in a musical keyboard. Use that keyboard sample to play the melody line over your background music. Keep a recording of that.
Then bring that track into your video editor. Remove the video's sound and only allow the music you wrote. Then, cut up little tiny clips of your video - like the cat mid-air for a few frames. Pick 1-2 clips per "song". Repeat that same clip every time the sampled horn plays a note from the melody, and occasionally vary the clip a little (zoom in, reverse it, or some other variation).
That's going to be a very tedious project as you suspected. It took me hours to make this video, but I used the 2-step process above (though step 2 was obviously somewhat different).