Parsad, I may appear too harsh sometimes, especially when it is about scientific topics. The reason is my innate passion, but I have huge respect for your and your work here ^^.
1) We now little about the brain, yes. But a lot about psychometry. That is the difference. We know the end results, but not much about HOW the process is that leads to it.
2) I understand giving you 800+ pages is too much. So if you are interested in a first glimpse:
https://infoproc.blogspot.com/2016/01/smpy-at-50-research-associate-position.html
Everything about IQ from Prof Steve Hsu is brilliant on his blog.
In short, IQ is HUGELY HUGELY predictive. The difference between top 99%, 99,9% and 99,99% is significant. And the world's best are extremely often 150+ in a lot of fields. IQ is in fact one of the best predictors of success in Math, Physics etc.
3) "But I've never felt particularly smart or intelligent" And a lot of people have an IQ of 90 and feel like geniuses who know everything. How you personally feel is uncorrelated to how high your IQ is. I bet Terence Tao does not consider himself a genius. But that is meaningless since he is.
I don't know what test you did. But to be very sure, I personally would just trust the Stanford Binet or WAIS done after 20 years of age.
Everything else could be imprecise IMHO.
I think to be an incredible genius of unlimited ability who is hardly ever matched, which you describe with "I've seen people from all walks of life at times do extraordinary things that certainly made me feel ordinary" you would need >160 on the SB V or WAIS. That means completely maxxing out every subcategory of the test.
Someone like Terence Tao or Ed Witten or John von Neuman could do that very easily.
But this kind of calibre is rare.