These are all related to questions about the perspicuity and authority of Scripture and the role of general revelation. After the Fall, which is traditionally understood as warping our moral and spiritual sense, can we still trust our senses and minds to discover truths about nature? You are right in pointing out that in the case of salvation, most Christians would say that without special revelation (Scripture), we wouldn’t know how to obtain salvation. We also need special revelation to correct our morals - we can’t just trust our conscience all the time. But does this skepticism apply to empirical science as well?
It’s been my impression that the Protestant Reformers were much more wary of trusting the human intellect compared to their immediate theological forebears. The result is more emphasis on the need for special revelation - in line with sola scriptura. Some people would take it further, like Van Til and his presuppositional apologetics, who try to argue that it’s impossible to reason coherently without assuming that Christianity is true. They are generally very skeptical of arguments from natural theology, including design arguments.
Similarly, some YECs will simply state that we can’t do science without being guided by Scripture, because our brains just can’t function properly. What I find unsatisfying about this stance is that most YECs would still trust the findings of medical science, engineering, etc. In addition, we also use the general tools of logic and observation to understand Scripture. Thus, I don’t think this general skepticism about our intellect can be lived out consistently. The scientific reasoning by which one deduces that the Earth is old is not different in principle compared to the reasoning by which we figure out someone has COVID, for example.
This also explains why YECs try to posit a historical versus operational science distinction and argue that the former is inferior to the latter. But I do not think their arguments on this are convincing either.
A second argument against this is that science has been immensely successful in constructing theories about the past, something which would be difficult to explain if our brains are completely fallen and twisted. For example, virtually all cosmologists (Christian or not) agree today that the universe is about 13.5 billion years old. Compare that to the state of the field of biblical studies, for example, which has a lot of disagreement even among Christian scholars who subscribe to the same fundamental beliefs and assumptions.