With regards to “1 Timothy 5:19 priests are said to have a certain legal privilege.” that having two witnesses was the usual standard of Jewish law, Deut. 19:15 requiring the witness of two or three persons. It was a standard Jesus repeated at John 8:17.
Why then repeat it to Timothy? Because of the presence of men like Diotrephes and others (Third John vs. 9) who bad mouthed even the apostles, (2 Cor. 10:10-12).