I wish duolingo could start adding kanji after we learn the hiragana to a word
Supposedly, kanji with furigana is an intended feature of the final version of this course. It is still in beta, but until then it is a little awkward with no external resources.
Why is it あたらしく, not あたらし?
Isn't あたらしく an adverb (which should modify a verb)? Since this word is modifying a noun (セーター), shouldn't it be an adjective (あたらし)?
First of all, it is 新しい, and second of all, in this case, what it's doing is making it into the negative form, which is "not new".