Why did he say "Chat'os Ne'urai u'Fesha'ai"?
Radak: Sins of youth are called Chata'im, for man's Da'as is not complete, and there is no Pesha, i.e. rebellion. When one is Mezid after 20 years, when he has Da'as, he is called Poshe'a, for he recognizes, knows and transgresses the Mitzvah. He rebels against the One who commanded about it!
Malbim: They are when I denied the good that You did, and I sinned. Sin is increased according to the Chesed [that he received]; it obligates to cease Chesed and mercy [for the sinner].
What is the meaning of "k'Chasdecha Zechar Li"?
Rashi: Remember what is worthy of Your Chesed - my good deeds.
Radak: Do not remember either (Chata'os or Pesha'im). Rather, remember his Chesed, and bestow to him according to his Chesed, and not according to his judgment.
Malbim: Remember for me Your Chesed that You did for me.
Why did he say "Lema'an Tucvha"?
Radak: Not for my sake, rather, for the sake of Your good and Chesed, that You are good and forgiving.
Malbim: Due to Your good, it is proper that You remember the good, and not the bad.