"Isn't it cute?"
かわいいですね。Is simply a statement. Adding a question mark to the end makes it a statement that requests confirmation. 'It's cute, huh' or 'It's cute, isn't it'.
かわいくないですか? used colloquially could mean, 'Isn't it cute?' rhetorically. However, it could also be interrogative, depending on the intonation and context.
'I'm not really fond of the new members of the group. Why not, are they not cute?'
I think this is a bad translation. In English, a negative question like "Isn't it cute?" assumes the answer will be "Yes, it IS cute." But I don't think Japanese uses negative questions the same way. Thus, the question we are asked should be "Is it cute?" To me, the answer Duolingo gave me (かわいくないですか) would translate as, "It isn't cute, is it?" This is totally different.
"It isn't cute, is it?" in Japanese can be phrased as「かわいくなくないですか？」or「かわいくないですよね」
「かわいくないですか」can be interpreted two ways and it depends on tone and pitch.
「かわいく、ないですか？」"it is cute, do you agree?" speaker thinks it's cute and asking for the listener agreement.
「かわいくない、ですか？」"it is not cute, right?" speaker thinks it is not cute and asking for confirmation.
Agreed. Without context, there's no reason to think that "Isn't it cute?" should be translated any differently from "It's cute, isn't it?"
My understanding is that Japanese speakers use negative rhetorical questions in much the same way that English speakers do, so the same ought to be true in the reverse direction with「かわいくないですか？」and「かわいいですね。」