Arm out or in the piano

I don't understand what you mean. The arm is doing a longer slower movement that cannot explain separate key movements. It's the lengthening of fingers that moves the keys. What else is left?

Oh ,when you say lengthening you mean the MCP rising up? I interpretate lengthening as just keeping the fingers straight and gliding on the keys...

No, the fingers are already at length in that situation. See the link in the other thread about playing during a down movement. It's an action, not a position.

To simplify: there are no down movements. Just make everything up and you will be fine! AFF

I agree in the knuckle, but surely there's a limit if we don't clarify up and down in the wrist? I used to have big issues due to being unable to separate them. My right wrist was constantly going up and getting trapped, which only weakened the capacity for decent finger movement. Recently I've been using an exercise which is effective at virtually any level. For any finger I practise repetitions during an upward wrist movement. It's not a push forward and in but literally just floating up. A beginner might start with just two repetitions from the finger and then carry floating out. At advanced level it may be six or more for each finger. Although that's by far the most common movement in actual playing, by doing the same in a downward movement it arguably teaches an even better distinction between wrist and knuckle. If you can get up to four or five repetitions in a down motion of the wrist, you know that you're not depending on this downward movement to move the key. The finger is still doing its job of lengthening into the key, even though the wrist is slowly sinking. It then tends to work even better still if you return to the more natural up movement. Also, for something like the Liszt 6th rhapsody you need to be able to repeat in both ups and downs in order to keep going for such a long time. Generally I start phrases already down and go up, but it's not always possible to get through a musical idea without having to go down while still playing. I still have to take care to ensure that downward wrist movements are not for the sake of doing the work of the fingers, but it's been a very important part of my technique recently to learn to move well on both ups and downs of the wrist, so I don't get stranded in an up position.