AAQ, the kuzari is uniquely passionate against the study of philosophy, which is the foundation of the derisha vechakira approach that some take. He says to have emunah based on mesorah, as I described above.
The rambam, who championed philosophy, also writes clearly that one may not undertake such an approach to emunah before learning shas and poskim. I don’t believe anyone among us is on such a level in our time.
Shlomo, I don’t think you understand my post. I’m not trying to prove the truth of our emunah. I’m supplying an answer to the OP’s first question, which is identical to the kashya rav yosef albo asked on the rambam’s inclusion of bias hamoshiach in the 13 ikkarim. Part of the answer to that question is that we have a chain of succession in authority as to what the ikkarim are – the same way we have a chain of command in deciding any other halacha question. Amoraim accept the tanaim, rishonim accept the amoraim, achronim accept the rishonim, and we grope in the dark to understand any of them.