I do not like.
Ich mag dich nicht.
If you were saying "I like horses", it would be "Ich mag Pferde". "I don't like horses" is "Ich mag Pferde nicht"
Ich will nicht translates as I don't want to.
Ich bin nicht da translates as I am not there.
Ich hörte nicht translates as I didn't hear.
Ich bin nicht deutsch literally translates as I am not German but is grammatically incorrect. The correct form is ich bin kein Deutscher.
Ich bin nicht ich means I am not me in English. A complete translation of the song can be found here:http://quizilla.teennick.com/lyrics/7735696/ich-bin-nicht-ich-english-translation
Ich hörte nicht translates as I didn't hear.
Weiss ich nicht translates as I don't know.
Ich bin nicht perfekt or Ich bin nicht vollkommen
das mag ich = I like that
ich weiss gar nicht was ich schreiben soll = I have no idea what I should write