Both "love" and "like" are correct translations in this sentence. In terms of context, "like" could be intended, but that really depends on the speaker's/writer's intention, which is unknown here. However, if Duolingo wants to only accept "like" as a translation here and not "love", then they should use нравится rather than любит.
Ignore the link. It's not wrong; it depends on how the speaker feels about it.
Why is art/искусство a completely different word than художник/artist? They don't share root. Why?
художник is a loanword, albeit an old one. Compare to modern English "handy" or German "handlich". It meant "skillful" in the source language (an understandable derivative of "hand"), which then got transformed into "art".
Искусство and вкус are also borrowed—from a different root that meant "to try".
It is most likely Gothic (for искусство, it came through Church Slavonic). There are other Gothic loanwords among the older ones, like хлеб or лук. That's why English and German occasionally have related words (eg., "loaf", "leek"): these are all Germanic languages. This said, the words were borrowed into Russian a long time ago, and the languages are more like cousins than fathers and daughters. Thus, both the pronunciations and the meanings often bear little resemblance across these languages.
As for the art... Come to think of it, art as human activity has many forms other than painting or drawing. It is just that in English "art" without any clarification is often used for works of visual art, and the person who creates such works is an artist.
Say that in English without using the word "love", and you'll have an idea.
Why is there a ь after л and before я? I thought л becomes soft automatically before this vowel.
It is in the Accusative here. The form is the same as the Nominative, and it is no coincidence.
Do adjectives based on proper nouns get capitalized in Russian? (in English it would be Italian art.)