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Is it possible to see the earth's curve anywhere on it?
Not from the land as light travels straight, and there are too many obstacles within our line of sight. But it is possible to realise it from heights in a plane or on a mountain. You will see that there are no conrners, which means it is a curve as it is not a line. Absolutely yes. The best places to see the curve of the earth is on the shore or on the ocean. It is possible to see it in the arch (although ever so slight) in long spanning suspension bridges, where the vertical bridge supports are not parallel. Other places on land is flat areas like Kansas or the desert where you can get a horizon to horizon view. On cloudy days, you can see the wrap of atmosphere as the distance to the horizion increases but the humidity has to be low for this to occur.
How do you calculate the radius of curvature for the curve?
See the following link.
What is a series of points that go on forever?
An open curve
How the sine curve related to a curve?
Basically, it IS a curve.
A imaginary line that follows the curve of the earth the shortest distance between two points on a globe?
... is called a Great Circle arc.
