Translation:He does not like to take the subway.
"He doesn't like taking the underground" A subway, in British English, is just a path that goes under a road.
Mm, that can't be... Duolingo makes these two interchangeable automatically everywhere. Are you sure there wasn't any other mistake or typo? What was your full input?
The metro is the worldwide standard term for the means of transit so yes.
Not worldwide; where I come from the metro is the bus system; where I live now, no one ever says metro; it is fairly common in some places, though and should be accepted.
Well, literally, yes :)
Actually we have another word for "take" in the sense of "taking train, bus, subway, etc.": 搭。
So "搭地铁" will be also perfect (but maybe more formal.)
Yes it's normal and more common than ''to go by'' ...to take the bus, take the car, etc