Any of you playing the piano ?

Just started learning piano about a month ago since I need to learn a secondary instrument in order to graduate. It feels great to be honest. Currently learning Bartok's "Mikrokosmos" and a few Hanon exercises with an excellent professor.

What I am seeking is somebody who could tell exactly what is useful or absolutely mandatory to learn.

Phrasing and rhythm are two very important aspects imo. Piano is a percussive instrument after all. Also, don't look down at first, read the notes on the page.
 
I took piano lessons for about a year and a half starting when I was 25. I learned a little bit how to sight read, some basic theory, finger patterns, and technique. I also learned that I can't keep two separate rhythms going at the same time. Not long after that I slept with my piano teacher and stopped going.