Is there a reason why do pianists have to "show-off" as they are playing?
Every person is different. Some pianists chose to do some acting to emphasize or support their playing, other can't help it (it's involuntary) and others focus only on the music. While the final music result is valid, the gestures are not important. I recall, for example, one of my favourite pianists, Uchida. She has really exaggerated gestures that I don't like visually but I find her playing just wonderful. I guess she needs those gestures while another giants like Cliburn never did an unnecessary movement or face gesture.
How can you transmit your feelings and emotions through music?
In my opinion there's no real art without a control over the emotions. Of course, also in my opinion, there's many emotion in music but there's also a science and composers write with many detail. Emotion must be never an excuse to distort the basis of music (tempo, dynamics, rhythm, phrasing...). Emotion = YES but CONTROLLED. You control the music, you control the emotion. The emotion mustn't control you.
Is it necessary to make gestures and move in a "sophisitcated" way or can it be only enough with how one plays the piano?
Be always yourself! Never do a movement you don't want to only because a well known pianist does it. But you must have in account that for what many of us we understand as a good technique, some movements of the wrist and the arm, not only the fingers, are absolutely necessary. You'll need them in order to play technically correct, releasing tension and helping the strings of the piano to "sing" and to phrase. These ones must not be confused with the external face gestures or full body contortions seen on some pianists. The first ones are necessary and affect directly and greatly to the final sound obtained. The second ones are accessories (I personally do not like them).
How can you transmit the "correct emotions"?
You must organize very well your study time and try to use always your brain and ear. Try to listen in real time not only to the sound you think you are obtaining but also to the sound is really sounding. Don't let that an excess of emotions blinds you and make that what someone thinks that is making a passionate rendition reality is an unintelligibly and uneven mess! (God bless home recordings, that wonderful tool to improve

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