Ok, Yesterday I was drowsy, so I couldn't tell more.
The teachers I had and have have always coincided that I need to learn first with hs before putting them together, and it may be because I have a poor study method by my own.
Before playing, I play some scales and cadences, not all of them, but some for at least 10-15 minutes.
What I do normally when I begin learning a piece is playing using a metronome at a fair speed (eg 60 bpm), before I used to play with hands together, but after seeing many teachers, I decided to play first separately.
Yeah, I also learned that playing hs is also to polish and improve the piece.
But another teachers, two to be exact, who are my solfege teachers, one related to musicians in general, another to teach to become a music teacher, have told us that playing the instrument is the last thing to do, one needs to listen the piece many times, then read the score, sing the piece and then sing it. They assure that with all that we can learn faster, but I have problems with that because my mind and fingers are not utterly synchronized.
And about time, I also have other subjects to which I need to pay attention: solfege, music history, education laboratory, harmony and sightreading. Every subject is asking and giving me tasks which I need to pay attention as well like my pieces. I know that all are related and each one has to help and support the other, but sometimes is difficult to apply all that I have learnt in one subject with another one, and specially with improving my piano technique.
I also heard that there are other students and people who can learn faster and get their pieces in just one week. Eg, a pianist needs to have a repertoire of one hour for a concert in one month, and in one week he/she learnt and got Beethoven's sonata op 2 no 1 with all the movements. In my case, doing that will take me more than 3 months.
As you say, I need to learn on my own and no one is going to tell me how to study in the end, but until now, until now, I have been with many teachers, and no one has told me how to get a piece faster, they at some point tell me not to rush but at the same time be faster, follow what they say, but also advance on my own even if they don't tell me, and don't pay attention to the other subjects, but to increase my ability even though they don't tell me how to.
What I only want is how to increase my piano ability and technique and also have time to the other subjects and my work in the future. I always work hard, but for some reason I am slower than others.