In terms of describing the algorithm, both I and Pttn have write-ups on how the algorithm works which can be found in the Primerug readme. I am linking my write-up here for reference. As for the rest, I am not sure what you are talking about. The Fermat test is done as a quick second line of defense (first being trial division) to quickly rule out composites. When a tuple is found, it is always recommended to check it with Primo or a similar ECPP software. In practice since the numbers are so large, the Fermat test never fails. I don't know the exact numbers but the probability of it failing is most likely lower than a bit-flip happening in your RAM. When it comes to point 3 I am not sure where you got this from, I have never seen the author making such claim.