[[Does any Church or Council possess infallibility or did Jesus alone possess this?]]
Well if a church or leader was really infallible, then I could pick and choose who I want to be my savior
You sure can’t rely on Rome because the Muratorian fragment represents the canon of scripture for Rome, c. 180 A.D. It contains the NT, minus some missing pieces, but also includes the Revelation of Peter, a Gnostic text.
The church in Rome sure was infallible all right as they had a Gnostic text within their approved scriptures. They went around declaring others to be heretics while they were arch heretics.