Their heads are not swollen or aching, just dizzy because they get up so quickly and run to the windows.
2. Doth - does
Doth is the archaic form of do. Does is the best option. I'm hoping that you just had a typo because the line with doth is saying that the light shines brighter than does the noon-day sun. If it's not a typo I'd guess "goes".
3. Amain - quickly
This is the best choice because the train is then described as being both quick and gone. It does not travel carefully since it is going with great speed and there is nothing to suggest that it is late.
i would say to introduce your topic to the reader so 4) and i don"t think it would be 2) because typically you only give background or state your points in an explanatory or argumentative essay
