Pater noster is Latin for the Our Father Matt 7:9-13. Note the following verses: For if you forgive men their trespasses, your heavenly father also will forgive you...
St. Peter was given the keys to the Kingdom - note the keys on the Papal flag and the authority to name men to the priesthood with the power, through the Holy Spirit, power to forgive sins. Ditto for other sacraments.
White probably means with, pronounced wit or long-voweled dialect. Every Christian child is brother to Christ and the Virgin Mary's child.
Early Protestant would be 1533 in England. Rev. Lumby is correct, it's a Catholic song, and not a "remnant" of Catholic Church at all. There are tons of references in folk songs and stories that are obviously Catholic but whose origin are obscure because of misspellings and ignorance. Catholic recucancy was a major irritant in Lancashire. Puritan recucancy didn't become an issue until 1559ish and certainly not in Lancashire.
Richard Wilson has written an interestin book about Shakespeare's recusancy. He's got a few things wrong - origin or the confessional box, for example. If ysomeone ripped something out of a church 400+ years ago you cannot complain they were never there or arose historically elsewhere.