How is it a fallacious argument from authority?
Because you are citing the survival of institutions of organised Christianity as grounds to believe Christian claims.
So if I tell my friend that I saw a paralyzed man get up and walk, and ten other people confirm that they saw it too, then it is not established as credible?
Nope - there are more prosaic everyday explanations to be considered first: you could be wrong, as could the ten other people, and that you would advance a miracle explanation at all might raise the risk of bias and credulity, and there is then the possibility that you were being misled in some way. So there are various aspects involving people and these are always more likely that anything supernatural since we know that making mistakes, being misled and misleading others are known human traits.
Given that something supernatural cannot be understood by natural creatures such as us your demand for a method to establish it is, I would say, a red herring.
Nope - if you are claiming the supernatural then you need a method suited to it else, as we have seen you do, you risk falling head-first into any number of fallacies: such as arguments from authority and personal incredulity, confirmation bias, special pleading and the negative proof fallacy.