Answer: That bit about the chords is an interesting one. "Amazing Grace" is a purely pentatonic melody, yet when harmonized almost everyone will use I, I7, IV, and V chords (e.g. C, C7, F, and G if the tonic is C). But those chords include notes, B, Bb, and F, that are not in the C major pentatonic scale C, D, E, G, A.

And that's OK. Because harmony has different requirements than does melody.

Both the pentatonic and major scale are diatonic - meaning that neither one contains chromatic steps, which are defined as the sort of steps in which the note letter name doesn't change - e.g. F to F# is a chromatic half step; F to Gb is a diatonic half step.

You could really say that our major and minor scales derive from harmony. Imagine yourself living a long time ago: Start off with something like pentatonic, a very old scale, and once you discover the concept of harmony you're going to end up adding notes to the palette.

In short, the scale police are not going to come after you if you use for a pentatonic melody the same chords you'd use in a full major or minor scale. Just do what sounds right. The pentatonic has an ancient feeling to it that may be just what you're looking for sometimes. Originally it might have been heard with nothing more than a drone on the tonic, or the tonic plus the fifth - but it can still be harmonized in modern style with the full set of scale pitches.