Yes, it should be accepted.

爬山&健行 means hiking, but they're not totally equal. 登山 means mountain climbing, with backpack and equipment. It's the different vocabuary have to remember it.

Most of the people I met while living in China used 爬山 the same way we use (very casual) hiking: going for a walk outside of the city, preferably involving a hill or small mountain.

Also curious about this. Guess I could ask some Mandarin speakers... Perhaps 徒步旅行 is more common?

I think there's a difference between "I really don't like" and "I don't really like". The former is putting the emphasis on "don't like", increasing the degree. The latter is reducing the emphasis of "don't like". Sometimes used when you want to be polite.