Biblical use of the word, "hymn"

This is not a profound post (not that any of mine are). I did a search for the word, "hymn" in the Bible. I discovered six uses of the word, all in the New Testament. Here they are (all from the ESV):

Matthew 26:30 And when they had sung a hymn, they went out to the Mount of Olives. Mark 14:26 is identical. The "they" is Jesus and the eleven apostles, Judas having left to betray Jesus to the Jewish authorities.

Acts 16:25 About midnight Paul and Silas were praying and singing hymns to God, and the prisoners were listening to them,

1 Corinthians 14:26 What then, brothers? When you come together, each one has a hymn, a lesson, a revelation, a tongue, or an interpretation. Let all things be done for building up.

Ephesians 5:19 addressing one another in psalms and hymns and spiritual songs, singing and making melody to the Lord with your heart,

Colossians 3:16 Let the word of Christ dwell in you richly, teaching and admonishing one another in all wisdom, singing psalms and hymns and spiritual songs, with thankfulness in your hearts to God.

A couple of conclusions, from an amateur:
1) Singing is appropriate, and important, in corporate worship.
2) There were apparently three types of songs used by the early church, all approved by Paul. I have no idea what Paul meant by a "hymn," or a "spiritual song," and how they might have differed. Perhaps the psalms were from the book of Psalms.
3) whatever hymns and spiritual songs were, someone must have written them, probably during New Testament times.

Thanks for reading.