"He goes to his parents."
Translation:Han tager hen til sine forældre.
Hen is "to". In English, this is often implied: I you ask "Where are you going", it's implied that you are moving somewhere. "I'm going to Scarborough fair." You would not expect the answer "I'm going over that bumpy bit just outside the town gate.", because "go" has already implied that it's about destination, rather than the exact route.
Regardless of what it says in your notes, "go" doesn't mean so much use a specific way to travel as the "travelling" itself, just with less of a stress on the torturous aspect of the experience. Try it for yourself: In English any time "go" is used in the sense of movement, use "travel" instead, and vv.. In Danish, the same word, "går", has come to mean more specifically travelling on foot. But that doesn't mean that English "go" will always mean "walk", just that you'd have to use a different translation for going from St Pancras International to Paris.
Yes, "tager" a destination can be used to mean "take a trip"/"travel", whereas "tager" with a noun is just "take". Of course, as with other expressions that have become separate meanings, there are grey areas, but context is your friend. And remember, this is a course to learn Danish; the English is just there to check you're getting the Danish right, so concentrate on the Danish, not on how it fits into English.
That is not quite right: "hen" indicates a direction, not a location. For a fixed location, you would use "henne". Example: "Hvor er den henne?" meaning "Where is it?"
Other adverbs follow the same pattern: ind/inde meaning in, ud/ude meaning out, where you use the first for direction and the second, with e on the end, for fixed location.
Again, another contextless sentence. While the discussion covers a lot of points, especially how one "goes", there is no indication of the intent. He could walk, skip, hop, take a bus, a plane or ride a turtle or duck. Another aspect is that it could mean "goes" in the sense that he goes to his parents for advice; would this have an even different translation?