https://www.whiteeagleaerospace.com/first-flight-over-the-south-pole/
http://www.classichistory.net/archives/first-polar-flight
And somehow they accomplished this without compasses working. Which later proved problematic in 1979:
https://www.history.com/this-day-in-history/plane-crashes-over-antarctica
If someone want to fly over the North Pole today, they can do that by taking a direct flight from New York to Hong Kong. Takes about 15.5 hours. Flies most days of the week. Expect tickets to be around $500-$1000.
Not certain if relevant to the topic of the post. There exist some other flight that does the same, but this is one of those that been operating for the longest, and gets you the closest to the North Pole.
Correct. People fly over the North Pole all the time. There however is little evidence that anyone has actually flown over the South Pole.
Yes. From Sidney to where the ice starts, there is about 2000 miles, which should take about 4,5 hours to fly. Once you are there, all you can do is turn around: so a total flight time of 9 hours. Anyone trying to undertake such a flight would need permission to do so, good luck obtaining such a thing. They probably going to make you pay insurance for a rescue operation, which easily could come down to $1.000.000.
Once at the ice edge, you could try and keep flying South, but it would not take long until you are in a land engulfed in constant darkness, with howling winds, and zero radar communication. Finding your way back to the ocean would be a challenge in itself: you probably would need a boat to stay in radar contact with, while exploring further South, to make sure you do not get lost over the ice. Boats sailing to far South will get intercepted by the Coast Guard, so again, need permission, which is going to cost a lot of money, for insurance of a potential rescue operation, or so they say.
Wonder how many people actually know you can fly over the North Pole though. I seen some pretty odd conspiracies in regards to what is at the North Pole, there being more land there, etc.