This is where I get confused. What is at a latitude of 45 degrees? .
So the circumference of the Earth is ~40,000km. Hence Pole to Equator is ~10,000km, therefore 5,000km, as you stated if you went south of the North Pole must be at latitude 45 degrees.
If the pole axis actually went south at that rate it should therefore be 'there' in 50 million years, but....
There have been 7 ice ages in the past 50 million years which means there could be multiple times when the ice could be receding or expanding, not just receding as the article seems to be saying.
...I believe they are saying that the movement in the past
100 years has been caused by the effects of the three factors that they discuss. And this has caused the axis to slip 10 metres south. So the effects of a warming planet and the last ice age unwinding are the current effects. They are not saying that these factors have existed continually in the past, nor that they will exist continually in the future. In fact I believe they will not - the main driver that makes the Earth oscillate through a range of axial tilts is, as I stated, the Sun and the rest of the Solar system. These movements that the scientists are describing are, I think, a tiny small perturbation that will not have a lasting effect.
So, for example in the immediate future, if Greenland was to fully melt there might be further slippage south, but perhaps in in the near future a new Ice age will 're-ice' Greenland and then the component vector would probably reverse and the pole would tend to go back north.
Unless the ice vector they drew takes that into account. The continents have moved around considerably during the past 50 million years, if the time period is 50 million years then the location they show at 45 degrees wont have North America in it the way the article shows it, if North America would even still be there.
I don't think the map they had was supposed to depict the Earth 50 million years from now. It looks too current!
The polar regions have been ice free in the past, maybe a couple of times in the last 100 million years. But when I read that, I wonder if Antarctica was ice free because it wasn't anywhere near the south pole but higher up in a warmer region.
Polar regions have certainly been ice-free in the past, although if they were just oceans then they will have little effect on the issue of axial wobbliness.
Antarctica and Australia split, I believe, about 50 million years ago, Australia heading north and Antarctica going south, where it is now over the south pole. Having a big plateau of land over the south pole certainly helped form a lot of ice.
If the physical axis is that far down where are the magnetic poles, do they also drift down or stay up on top so to speak. If they start to go towards the equator would they inclined to flip polarity. Do they flip every couple of degrees the axis moves. Are the magnetic poles pointed "upward" controlled by the sun or can they be at any latitude. The magnetic poles have flipped on average every million years for the past 65 million years.
How the magnetic poles work is, I believe, still a problem to solve. Largely I think because we know so little about what exactly is happening deep in the core of the planet. So I'd guess the answer is that we don't know what is the main factor that drives the magnetic field of the Earth.
But yes the magnetic field regularly flips, as we can see that in geological record.
Although there must be some connection with the actual spin of the planet, the magnetic pole wanders about much, much more. See this:
Why does the North Pole move?
Unless there is a massive collision with a huge astronomical object I can't see the Earth's axis of rotation deviating beyond what we know, i.e. the 21-24 degree wobble and oscillation of our axial tilt.