Hi Jan, welcome to the forum family!
Yeah, most of us here are into classical music, but you will find others like you who also like modern stuff. But when you get right down to it, it's all the same no matter how long ago the music was written. Eventually you only have two categories- good music and bad music. I prefer stuff from the Romantic period, but the things I like most about this time period, I can also find in pop, jazz, and big band music. Dont be afraid to explore your interests. Perhaps this music you learn for yourself -stuff from George Winston, Yann Tiersen, etc. you like for a certain reason, whether it be for the melodies, rhythm, or motifs... whatever it is, I am sure you can find the origins of the fascination in some form of classical music.
I was really interested in how you seem to separate "practicing" a piece from "playing" it. I dont know, ...I tend to practice playing the piece!

Usually my ear can tell me when something sounds bad or if I am not steady in a certain passage, and from there, usually I can will myself to slow down and make sure each note is heard, playing hands separately, voices separately, etc.. If I dont catch my own mistakes, I am confident my teacher will and can set me on the right path.
But dont sit down on the piano bench and refuse to put a piece of music together because you are "practicing" it and are afraid to mess it up. The first time you open up the sheetmusic, do not be afraid to attempt playing it as if you were performing it. If you didnt, piano and music altogether would be so boring you would not want to play any more than others would want to hear you.
now playing: some Allegros by Bach (in my lessons, for "gaining advanced finger control") and Thanksgiving by Winston (private)
haha no need to be so "private" with your interests! What, are you afraid your piano teacher will beat you if they found out what you have been up to?
Smile,
donjuan