Oh, and by whose or what authority did they designate teachers?
By your own words, you admit that the Apostles provided both successors and a manner in which to chose them.
>>Oh, and by whose or what authority did they designate teachers?<<
I’m not sure there is any record by the apostles other then those who were the most learned and those most hungry who learned from the apostles themselves. Jesus did tell us that some are called.