Let me pose some of your own questions to you. Have you ever been to the "center of the world"? Have you seen this magnetic mountain? And anyone with any basic knowledge of electromagnetics would know why compass needles point north, and why magnets magnetize. And no, I have not personally been to Mars, but have a basic knowledge of most of the planets in our system. However, this is not a debate about Mars (I do not know nothing of its atmosphere, however). And true, Antarctica is a place of much study, with several laboratories and such. But it is not some little icy island. I take it you don't do much travelling.
Ok, why do compass needles point north? No matter where you are on earth the magnets align to north/south. If the earth were a flat disc and there was a magnetic mountain in the middle that would make sense. If there earth were flat with a Sky Dome then it would make sense that polaris is in the middle and the sky rotates around it.
There are pictures of ice walls, ancient maps with ice walls and people have been believing the earth to be flat for 1000s of years. Everyone knows Antarctica is made up of a bunch of ice walls. Now, why is the earth FLAT?
Compass needles point north because they contain a basic magnet. Earth, like many other planets, has a core that is under immense pressure, made of liquid iron-nickel (temperature about 5700 K). The electrons align to form a giant magnet. The interaction of the comparatively weak magnetic fields of the compass interact with the much stronger magnetic fields of the core, causing the compass to align with the poles. The inner core's intense magnetism is also what protects Earth from intense radiation bursts and electromagnetic storms; without an active core Earth would look a lot more like Mars; barren and desolate.
If Earth were a flat disk with a magnetic mountain in the center it'd have to be one whopping big mountain, made of pure iron or tellurium or something, to have such an influence on magnets.
If Earth were a planet with no "sky dome," that orbits a star, stars that are hundreds of light-years (approximately 434, in Polaris' case) away would appear to move drastically.
Need I remind you that ancient maps also depict Europe, Africa, and Asia as the only continents, and have many cartographic errors. The advantage of modern technology is that it is
modern.
True, there are pictures of Antarctica's mountains and coast that have a few ice walls. However, there are also ice walls at the arctic ice cap. That doesn't make Earth's shape that of a CD. There are also many, many pictures and maps of the entire Antarctican landscape, with no edge of the world phenomenon. The pictures to which you're referring, if taken by a reliable source, also indicate that Earth is not a disk or table, but a sphere. Your own sample is evidence for the law that opposes your 'theory.'