Death to self and bear fruit!?

Our SS class has been discussing Matt. 7 and our conversation this past Sunday was about the narrow gate that few enter vs. the wide road that leads to destruction. We discussed dying to self, bearing fruit etc... I have been struggling with this conversation for several days now so I will explain. My dilemma: Is dying to myself a taught characteristic...something that I need to be taught and learn? Or is it a natural result of my learning who God is and my relationship growing with Him and my realization of who I am without Him? My second dilemma: Is the bearing fruit that is being talked about in Matt. 7 referring to making new believers or is it talking about the fruit of the spirit? From my short amount of time studying this it seems to me that the good tree bearing fruit is referring to the fruit of the spirit. Peace, Love, Joy, Self control.....Is that the fruit I should be leaving behind? Am I that kind of tree? I've been studying Heb. 11 and it seems that to produce that kind of fruit will require great sacrifice. Tami and I continue to consider what this means for us?!? Are we understanding God's word accurately? We are challenged by this and are seeking where we go from here.....the roller coaster has left the building!!