A few questions

[GundamZero]

Well, I am a Saint, and we ought to hold ourselves to such standards.(Little sermon for the road.)
But I digress.

I read a few of the comments on the leadership of the Church in Jerusalem. After reading the scripture referenced, I do not believe that this clearly proves James's supremacy to Peter.
However, it would make more sense if the authority of individual churches were left to specific leaders for the simple reason of running the churches affairs. There is nothing that says that Peter was under James's authority or Paul under Peter's or otherwise. However, this is just my hypothesis.

 

[DivineNames]

With Muslims who deny the authority of hadith, I would say that they are looking suspiciously like heretics because Islam has historically accepted the hadith as an important part of the religion. Perhaps they could provide good reasons to reject the hadith, but the burden of proof is on them I would say.

With regard to Christianity, if tradition has historically been regarded as a source of authority, then if certain Christians want to go against this principle then I would say that the burden of proof is on them to show that they have the "true" Christianity.