My theory on the squealing wheels on the curve:
The concave train wheels (the main, big ones) ride on the rails and make contact on the whole upper surface of the rails. When the rail curves and it is flat, there are longer and shorter arcs on that rail, around the curve (red is longest, blue is shortest, green is somewhere between). A wheel can only spin at one speed at a time. So one single wheel, would need to cover three separate distances, while only spinning at one speed*. That's impossible. So there must be some slippage occuring when the rubber hits the rails. So, if for example the wheel rolled at the correct speed along for the green arc, there would be some slippage along the red arc, because the wheel is doesn't turn enough times to cover the additional distance of the red arc. There would also be some slippage along the blue arc, because the wheel spins too many times for the shorter distance of the blue arc.
Slippage of some of the rubber on the rails = squealing

*There aren't just 3 arcs. There's an infinite number of arcs. I just used three to make the image. I could have drawn many more arcs with many more colors. And this picture just represents one of the rails. The wheels are probably squealing on both rails.