Du is used if you (singular, of course) is the subject of the sentence, while 'dig' is used when 'you' is the object of the sentence.

It should be marked as correct, since both den and det mean 'it'. I don't know why it's marked as incorrect, maybe it's an error made by duolingo? I'm not a native speaker though, so if I am wrong, someone correct me.

You only really use "den" in Danish if it is clear what you are talking about. "HundEN er sød. Jeg fortæller dig om DEN"