He told them they condemned him to be crucified. Which they did when they chose Barabbas to go free instead of Jesus. Which hearkens back to Leviticus, by the way. And his hearers knew then that they had done this to the one Person who could save them, their Savior, even God Himself, and that's why they were "pricked to the heart" ~ convicted internally by the Spirit.
Absolutely not. Not in the truly salvific sense. But his exhortation was not in that sense. Peter knew very well that the initial act in salvation is on the part of God via the Father's call and the Spirit's work in the heart of those called:
"Blessed be the God and Father of our Lord Jesus Christ! According to His great mercy, He has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead, to an inheritance that is imperishable, undefiled, and unfading, kept in heaven for you, who by God’s power are being guarded through faith for a salvation ready to be revealed in the last time."
[1 Peter 1:3-5]
"His divine power has granted to us all things that pertain to life and godliness, through the knowledge of Him who called us to His own glory and excellence, by which He has granted to us His precious and very great promises, so that through them you may become partakers of the divine nature, having escaped from the corruption that is in the world because of sinful desire. For this very reason, make every effort to supplement your faith with virtue, and virtue with knowledge, and knowledge with self-control, and self-control with steadfastness, and steadfastness with godliness, and godliness with brotherly affection, and brotherly affection with love. For if these qualities are yours and are increasing, they keep you from being ineffective or unfruitful in the knowledge of our Lord Jesus Christ. For whoever lacks these qualities is so nearsighted that he is blind, having forgotten that he was cleansed from his former sins. Therefore, brothers, be all the more diligent to confirm your calling and election, for if you practice these qualities you will never fall."
[2 Peter 1:10]
At the very end of that 2nd Peter passage (the last sentence, emphasized by me), he's basically repeating what he said in that verse that you cherry-picked from Acts 2 (verse 40).
Well, I'm very disconnected from what you apparently think Peter to be saying, but that's a good thing. :)
Grace and peace to you, Truther.