I commend you for exploring these epistemological issues, but I don't think you are going deeply enough. All the questions you ask are fine, but if you really want to get at the heart of the issue as it actually is in reality and practice, you need to look towards your own self. Is falafel infallible? I'm guessing that you would answer no. Thus, it doesn't matter whether any or all of the informational sources you listed are infallible, because you as the receiver and processor of those informational sources are not infallible. So, even if it could be proven* that Scripture was infallible, it wouldn't matter a single iota except in theory. Even if the Church was the infallible interpreter of the infallible Scripture, it wouldn't matter an iota except in theory. Unless someone is going to come along and claim that they are infallible themselves.
Put another way, if someone was infallible, or at least insightful enough to recognize and verify that something was infallible, then they wouldn't need the Bible in the first place, because they would already have the answers; but of course we know that no one is like that (Catholics don't even make that claim about the Pope, but greatly restrict under what circumstances he is considered infallible). If a person is not infallible, on the other hand, (which includes all of us) then it doesn't matter whether something like the Bible is infallible or fallible, because either way the person can expect to make mistakes, misunderstand reality, etc. Infallibility is, in my opinion, a word that never leaves the realm of theorizing, for it is impossible to do so except perhaps in the mind of an omniscient God (if she exists).
I know this isn't an orthodox answer, at least according to most, but I think it will save you a lot of trouble if you just cut right to the end. I ran my head through the ringer many years trying to figure out such epistemological points, only to realise that the answer was exactly in the opposite direction than what I was searching. Anyway, that's my 2 cents.
* Which it can't, without either using circular reasoning, or relying on a fallible authority to verify the supposedly infallible authority.