True Repentance

What does it mean to repent? Can a person repent without someone telling him to repent? Did the Apostle Paul repent when Jesus appeared to him in Acts 9? Did the Lord tell him to repent? Did the eunich repent in Acts 8, before Philip led him to the Lord? Did Philip tell him to repent? What about when the Apostle Peter was sent to the household of Cornelius? Did Peter tell them to repent? We know they got saved and filled with the Spirit while Peter was preaching. He didn't even give an altar call. In Acts 3:19, Peter said to repent and be converted. What exactly does that mean? In Mark 1:15, Jesus said to repent and believe the Gospel. What did He mean by that? We need a better understanding of what it means for a lost person to repent, and for a Christian to repent. In Revelation 2, the Lord Jesus told the church at Ephesus that they lost their first love. What does that mean? Should we examine our lives to make sure Jesus is still our first love? Jesus gave this church an A plus for their good works, but still rebuked them! Is there something else we need to understand?