This is a fairly standard Flat Earth map. It's not accurate (given the aforementioned statement about mapping), but it reasonably represents what most Flat Earthers believe about the shape of the Earth.
There is no "south pole" as such. Everything south is the "south pole", although in reality, there is no actual South pole.
There is a national treaty between some 50+ countries banning ordinary people from exploring Antarctica. Typically, governments will require a licence to explore, and once a licence has been obtained, there are limits and fines applied to control one's access to limit exploration (or perhaps artificially end it). The very fact that 50+ countries needed to sign up to enforce the Antarctic treaty is evidence of the size of it.
Jarle Andhoy was one such Antarctic explorer demonised by authorities for his attempt to explore Antarctica without a licence. And on one of his exploration journeys, his ship was lost at sea under suspicious circumstances.
https://www.outsideonline.com/outdoor-adventure/exploration-survival/what-really-happened-berserk/
I believe from accounts there is an ice wall at Antarctica, but people could explore beyond this (if they weren't harassed by governments). There are some unverified reports that government sponsored missions have journeyed far beyond the ice wall and come across "sky ice" which sublimates rather than melts, but although I believe some of these reports are likely true, I'm not aware they can be proven.
I believe there is land underneath Antarctica - ancient maps are evidence of this.
I don't know which natural laws comport to the Flat Earth model, but I would argue the law which states that water always finds its own level is a natural law offering strong evidence against a ball Earth.