"Sometimes" and "some times" have different meanings. If they are two separate words, then you are counting those times. Look at it this way: "There were times in the year when the rain was very violent." As this happened several times but not always, he expresses it using "some times" (as opposed to "all times", "many times" or "no times").

Good question. Look up "at times" and see what it means. Here specifically, you should understand it as "at (some) times", so the point is not "some", which is just an ordinary adjective here, like "at several times", "at a couple of times", etc. And for your bonus information, some times = several times. Eg, I did it (for) 5 times. You could say, I did it (for) several times. I did it (for) some times. "Some time" means A, a period. A period of time; B, a time (usually) in the future. I will go visit you some time.

"Sometimes" means every so often or from time to time.