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Also know, why does paper have margins?

In typography, a margin is the area between the main content of a page and the page edges. The margin helps to define where a line of text begins and ends. When a page is justified the text is spread out to be flush with the left and right margins.

Additionally, are you supposed to write in the margins? They write to the end of the paper. I had a steadfast belief my whole life up until now that the margin should not be written past unless you have to finish a word and if the word is long and you know it won't fit before the margin you take it down to the next line.

Similarly, you may ask, why are there red lines on lined paper?

It is removed by copiers to allow you to appear as though you have great straight line handwriting. The red line is a separate "channel" that can be removed as well independent of the blue lines. Non-photo blue is much lighter. Plus, lined paper predates the photocopier by a century.

What is the red line on notebook paper called?

It's called the margin line.