Welcome! Your son may well be gifted, but it's not certain. Notice that almost everything you've listed here is memory-based, and then think about the amount of memorising that every child does at this kind of age, learning their native language(s); although it's unusual to know so many things normally known only by much older children, and seeking these things out (rather than being heavily encouraged into them) suggests giftedness, it isn't conclusive.
So I'd caution against making firm plans on this basis right now. Find out as much as you can about the schools available to you, find out about homeschooling, and decide later. If there's a good kindergarten available to you, it might be useful, even if not for academics.
I can't resist pointing out that here:
Plural forms of most animals (e.g. geese, oxen, octopi.)
your son has been misinformed: the plural of octopus is not octopi (because the word isn't Latin in origin). I think have heard a case made for octopodes, but in reality the plural of octopus is octopuses.
