At the beginning, I could not play fast and cleanly, until I practice as stated below :

1. Play slowly first.
2. Play with rhythm, but slowly.
3, Play all right notes stacatto, slowly then play faster and faster.
4. Play phrase by phrase until you can play fast, then combine two phrases.

My current state is that I haven't practiced since I was a teenager, and I've just been playing whatever I liked - some things I played as a child, some new things, since we bought a piano some years ago. I'm looking for advice about effective ways, be it practicing passage by passage, practicing very slowly, or superfast, or with my hands crossed, or filming myself.
The sample was really only that, a sample to show my current ability, with a piece that is probably pretty typical of what I tend to play. It was only to give everybody an idea of the bad quality of my playing in case it made a difference for any advice - some people may benefit more from slow scales and others more from Chopin etudes at double speed. That I played it ages ago isn't even so important, because I didn't play it better back then. I understand that the minimal difference between pieces I've played for a long time and pieces I see for the first time is exactly because I never practiced - not during the last years, and probably not well as a teenager. So it's not specifically about how to perfect this piece. If practicing a concrete piece, slowly and so on, is good advice, this is something to take seriously. That's why I'm asking the whole thing. Could as well have been that everybody tells me not to touch any "real" composition and first practice nothing but Hanon for two years.

If you want to learn this piece properly, you need to practice the sections or bars in which you're stumbling over or not coordinating your hands. Take them out and practice them slowly by themselves (after making sure that your fingering works for you) until you get them right 100% of the time before gradually increasing speed back up to tempo and putting them back into the passages.

Without teacher, you'll keep making the same mistakes without knowing why (ingrained technical problems, rhythm problems, coordination problems etc).

If you do want to play advanced classical pieces to a high standard, you cannot do that without a good teacher. Of course, if you just want to have fun playing what you like, you don't need one.