According to Jesus, Those who believe and get baptized shall be saved. Those who don't believe ( that includes that sins are remitted in baptism per God's word) are damned already. Belief and corresponding action result in people being saved. The following conversion experiences speak to fact that being baptized in water in the name of the Lord Jesus is not optional. (Acts 2:36-42, 8:12-18, 10:43-48, 19:1-7, 22:16)
Acts 2:36-42 - When a person has been born again (Ezk 11:19-20) God exchanges their stony heart to a heart of flesh (a heart of flesh is soft and has a spiritual conscience that can be pricked by God).
When Peter accused these Jews of crucifying Christ, they were pricked in their heart, and said 'Men and brethren , what shall we do? We can compare this with the heart of stone of those that were "cut to the heart" and stoned Stephen to death for preaching the same sermon that Peter taught. (Acts 7:54).
Acts 2:38 - Peter told them to be baptised for (unto) the remission of sins. The remission of sins took place on the cross (Matt 26:28).
1 Pet 3:21 - The like figure (Noah being saved from drowning) whereunto even baptism doth also now save (deliver) us from our guilt, as baptism is an answer of a good conscience toward God. Save, according to Greek interpretation means deliver.
1 Pet 3:21 applies to all of your other scripture references.