Dear friends; as stated above, these things the Bible CLEARLY teach and anything contrary are merely the doctrines of men. WHERE in the Bible does it say that ALL one must do to be saved from his/her sins is "BELIEVE"? But, Jesus declare AFTER He established His covenant with the blood of His own death; "He that believeth AND IS BAPTIZED SHALL BE SAVED" Mk. 16:16. The thief lived and died under the covenant of Moses to which he was accountable until Christ's death Heb. 9:16-17.
Name even ONE command or example of a "sinner's prayer" in scripture for us to learn from. Name even ONE verse containing the words "FAITH ALONE" or "FAITH ONLY" besides Jms. 2:24, which tell us that NO ONE can be saved by "FAITH ONLY". As for infants and children, they do not need baptism for the forgiveness of sin. Because, they are born sinless Rom. 9:10-11 (sin is the violation of God's law 1 Jn. 3:4). Unborn and young infants can't do this and do NOT inherit the guilt of the sins of their fathers Eze. 18:20.
Now, regarding the Philippian jailor, don't stop reading at Acts 16:31. But, go all the way down to vs. 33 where the jailor and his family, AFTER hearing the gospel (by which faith comes Rom. 10:17) was immersed for the forgiveness of sins.
As for the use of man-made instruments of music in worship to God in the Old Testament; the Old Testament mentions the use of even by the children of Israel (i.e. Jews) of fire, oil, lambs, bullocks and cakes, etc. But, that does NOT make them relevant to N.T. Christian worship to God any more, OR LESS than the inventions of David Amos 6:5.
Nevertheless, this is a plea to CONSIDER THE TRUTH of God's Word over against opinions, theories and mere doctrines of men. Who is it among so many that will with a fair mind and sincere heart, search the scriptures DILIGENTLY to see whether these things are so?
"These were more noble than those in Thessalonica, in that they received the word with all readiness of mind, and SEARCHED THE SCRIPTURES daily, whether those things were so." Acts 17:11