The words to "Morning Has Broken" were written by Eleanor Farjean, copyright 1957. The tune is listed as a "Gaelic Melody" in some Protestant church hymnals. I'm not sure which Cat Stevens album it was recorded on--I think that is what helped popularize it in recent years.
"Simple Gifts" is a Shaker hymn. The Shakers were a celebate sect that used dancing ("shaking") in their worship rituals. I'm sure there are 'catteers with more info and links about them. I like another of their songs, "Come Life, Shaker Life" which can be sung in a round and makes me feel like spinning and stomping around.
There are several versions of the "Riddle Song", which one are you interested in? One starts, "I will give my love an apple without e'er a core", another, "I gave my love a cherry without any stone." Both traditional, as far as I know, which is not nearly as far as Bruce O!