That's just an assumption, an opinion.
It enjoyed authoritative teaching authority.
No it didn't because Jesus was still walking the planet at that time and HE was the authoritative teacher.
When He left, He gave believers the Holy Spirit as the authoritative teacher, and Scripture was available.
The church had no power, however, until the day of Pentecost as the Holy Spirit had not come yet, so the church could not have had authoritative teaching privileges.
And it must still exist.
Of course the body of Christ still exists. Where ever there are believers there is the church.
And It must teach inerrant doctrine, since God is truth.
Only Scripture is inerrant. Any one person or groups interpretation of Scripture for doctrine cannot be inerrant because God is beyond our comprehension. To claim that one's doctrine is inerrant is to lock God in a church box.
This is the quintessential example of what I referred to in my last post.
This assertion has no more biblical authority than a Cambell soup label. In fact, it is incredibly stupid.
One can not say Scripture is inerrant, but somebody's interpretation can not be inerrant, unless the person saying so claims inerrancy.
Such a person commits the same act they criticize the Catholic Church for, but simply isn't smart enough to recognize that fact.