It's not wrong. But remember, as "shriramkmurthi" said, the answer is checked by a computer, not a person. And what I have learnt till now about Duolingo is that he does NOT like abbreviations. So, if you want to keep your hearts, you'd better use "do not", "does not" or "I am" instead of "don't - doesn't - I'm"! ;-)
Other than the fact that "don't like" is not quite the same as "dislike", remember, there's a computer checking your answers, not a human. It may just fail to recognize that these two are roughly the same. Duolingo does so well that it can be easy to forget that it's all just algorithms and data underneath. (-:
Yes, but mich and mir are in different cases. "Mich" is in the accusative case, so it's the direct object. "Mir" is in the dative case, so it's the indirect object.
"Siehst du mich?" (Do you see me?) In this sentence, "mich" is the direct object.
"Ich bringe mir den Ball." (I'm bringing me the ball.) Who is bringing something? "Ich", which is the subject. What is being brought? "den Ball", the direct object. To whom? "Mir", the indirect object.