How bad is it to play with a raised wrist? By raised wrist, I mean that instead of being aligned flat with the forearm, the hand droops downward (so that the first set of knuckles are below the wrist.
I think the answer to the question is, if you're doing something that leads to an injury it could be really bad. If you're not then the worse thing is that your playing may suck compared with using your wrists [and the rest of you] to get the sound you want.
However, if something is going to cause an injury, unless you do something really dramatic [i.e slam or hammer your arms around] you should feel that it's not right. The caveat is not to ignore mild discomfort or pain.
Your focus is on the wrong thing, You need to consider movements in terms of how they feel to you, and how the sound created matches what you want to create.
[Since you mentioned using a computer, you might want to consider the movements you make using that too - perhaps you ignore pain during a tense quake 3 deathmatch - I know I have in the past or something similar, or perhaps your shoulders are tense, your seating wrong...once you focus on the way you feel [and again I mean senses not happy / sad etc] to play the piano, you may notice tense shoulders when you sit watching TV or you lean at an odd angle when using the computer because of where the monitor is, stuff like that]
It needs to be focussed in that sense. You can't listen to what noise the piano makes and then think "Oh, that was nice" you need to want a specific sound and aim for it. This is similar to other areas of practise where you need a goal and a purpose to make the practise effective [contrary to some schools of thought that suggest playing exercises when reading a book, so YMMV here, but you have to try and see what works]
So, it's not "nice sound" nor is it random effects that you decide after playing them that they were good. It's real things like dynamics "ppp, pp, p, fff" and so on and things like staccato, legato etc etc in a controlled sense that you wanted to achieve and then do. So you get what you willed to get. If you don't then you correct your movements until you do. Obtaining the right sound will require different movements.
Conclusion : there is no correct movement per se, there is a movement to get what you want to achieve with respect to the sound. Movements that are efficient and are comfortable for you and thus won't lead to injury or fatigue if you use them and will in time allow you to do fancy pants virtuoso pieces and play in a controlled way.
Finding it is an experiment + knowledge and experience. Experience in the sound means listening to lots of music and developing your ear. Experience in movements means "listening" to your sense of touch and how the movements you make feel.
What I think is wrong is somehow trying to concentrate on some specific paragraph of text you've read about rotating this and that. Use that as a guide for an approach, but concentrate on your movements in the sense that you concentrate on your hands and you can feel what they touch when perhaps you normally ignore much of it. How warm they are, your shirt rubbing against your wrist. Concentrate / focus on your playing mechanism in that sense, when you're trying to recreate the correct sound for how it feels. That's what I think it's about.
The teacher is to provide knowledge and experience beyond your own. The more diverse your experiments the more you learn. Think about playing a passage to make it have some emotion "happy / sad / angry" as well as some specific dynamic or effect. The more you interpret the piece or a segment of it the more you'll be in command of the movements you need to make to get those effects and thus recreate those emotions. That means there's no real "correct" movements per se for playing CDEFG, it's about what you want it to sound like. What impression you want to make.
The theory is that eventually the movements become as automatic as using a knife and fork - at that point they might be similar in that respect, but the way there doesn't seem at all similar.
If you play different notes then that's different movements too, so the difficulty and variety of the pieces you tackle will lead to more movements to discover and learn.
You need a teacher though...but I wouldn't worry about your teacher's knowledge of anatomy, they are a shortcut to experimenting and someone to say when you are right amongst teaching you other things.
Why your anatomy is interesting is only as far as science may justify the movements - in much the same way that a knowledge of how the brain works may tell you and / or justify a certain way to practise or learn efficiently. Neither are necessary for a teacher [or even you] to know though, not if they know the methods themselves. e.g You don't need to worry about physics to drive a car, you feel it, even if the underlying methods of
get out of my "£$"£ing way driving are grounded in physics.
You need to worry about your teachers ability to demonstrate and correct your playing in terms that give you some pragmatic goal to aim for to improve in piano playing. More important is that you buy into their philosophy for learning the piano - e.g some will say "do lots of exercises" others, as you see, don't...you can try both and see which works, but if you make your mind up, you need a teacher that agrees [otherwise you'll be ignoring them]
Topic: Hand deviation