Many passages make it clear that the requirement for salvation is to believe that Jesus died for the remission of sin and to personally accept His death as payment in full for our sins. As for the verses you’ve cited;
There’s controversy surrounding Mark 16:9-20. Most good study Bibles will contain a notation that the earliest and most reliable Greek manuscripts don’t have it, and the claims it makes for believers are suspect. Personally, I don’t think it’s a reliable passage for making doctrine.
Acts 2:38 Like John the Baptist, Peter advised his Jewish audience to repent. That meant that they were to change their minds about the need for a Savior to redeem them instead of relying on their obedience to the Law. To repent means to change one’s mind about something, to turn away from it. As we’ll see in our look at 1 Peter 3:18-22, Peter is using baptism to represent the entire salvation experience. He didn’t intend it as a requirement for salvation, but as providing evidence that repentance had taken place.
In 1 Peter 3:18-22 Peter is speaking of symbols. The flood symbolizes baptism and baptism symbolizes salvation. In reality the flood waters didn’t save Noah’s family. It was their faith to build the ark that saved them. And in reality baptism doesn’t save believers, it’s our faith in the death and resurrection of Jesus Christ that saves us. In both cases Peter used the water involved to symbolize the entire event.
In John 3:5, the context is being born again. The first birth is the water birth, the natural one where the baby is born in the birth water of the mother. This is where flesh gives birth to flesh to give physical life. The second birth is the spiritual one, where the Spirit of God joins with our spirit to give us eternal life.
None of this is meant to discourage or cast doubt on the practice of Baptism. It is intended to show that Baptism is the public confirmation that a private decision to accept the Lord’s death as payment for one’s sins has been made. While it often accompanies salvation, it can neither substitute for a personal decision by its presence nor can it invalidate such a decision by its absence.