A quirk is an unexpected trait or characteristic. Fate is how things are supposed to work out. A quirk of fate would be fate working out in a way that would be completely unexpected. For example, you would expect a fear of people to be a life long trait, not something that disappears by joining the Army. It worked out in an unexpected way, and he lost that fear. Hope that helps...

One speaks to the nature, and the other the process. In the end, the difference is so minor, they could easliy be used interchangebly.

It's not so specific. Usually refers to a time starting after midnight... when it ends is less precise. I think normally the use is referring to the fact that the activity carried into that early part of the day, and when it ended is less important. It literally means the little hours (small numbers 1,2,3...) 1. "late" and "very late" work. Though it's not really the same. They doesn't always mean until after midnight. Wee hours always means after midnight. So it might be more accurate to understand it as meaning "until early the next morning"... 3. It is generally plural. Hope that helps.

The most likely meaning would be with "case" as a noun. The "case" would be a box or container something would go in. The question would be asking is you see the box or container another thing goes in. Hope that makes sense...

It means something that is like the majority. A run-of-the-mill underwear company would make nothing special. They would make the same thing as 90% of the other companies. Not sure of Spanish...