If, someone proves something, it's proven right then and there, even if it takes years for people to understand it, or for it to make its way into textbooks. This stuff really is very obvious.
and, for example - if you are using one specific LEGAL definition of a genocide then you have to prove LEGALLY, following the regular process. if you're not doing it, then it's per definition not a proof.
Nope. There was a pretty smooth transition from "Nobody has ever wondered about this" to "All educated people know it's a ball shape" a very, very long time ago.
Eratosthenes comes up with a pretty good approximation both for how big the ball is, and how much its axis is off (you also if you think about it realise the planet must be spinning, that's why there's a day-night cycle)
Flat Earthers are a weird modern thing, they aren't somehow a remnant.