The three sentences are grammatically equivalent.
However, the interrogative pronoun che is very frequently reinforced with cosa; however, che cosa is often simplified into cosa in spoken language.
Why the pleonastic cosa is attached to che? Quite likely because it underlines the interrogative role of che, which has several other functions in Italian.
In the spoken Tuscan language that Manzoni studied for his definitive edition of “I promessi sposi”, dropping the che was frequent and Manzoni removed the che in most instances. One can find just che as interrogative pronoun in the novel, but only in narrations or when said by high level people: Manzoni wanted common people in his novel to speak like common people in Tuscany at his time.
Why is Duolingo correcting your grammatically correct sentence? Because the form with just che doesn't belong to current commonly spoken Italian, where che cosa or cosa would be used. In this case, per che may be confused with the interrogative perché. Not the specific case, where perché would be meaningless; but per che si vota oggi? (found in the comments) is very different from perché si vota oggi?.
This doesn't imply that you cannot use che in that or other contexts. Depending on the Italian region you're in, you can hear any of che vuoi?, che cosa vuoi? or cosa vuoi?, even by the same speaker in different contexts.
See http://www.treccani.it/enciclopedia/cosa-o-che-cosa-che_%28La-grammatica-italiana%29/ for more information on che/che cosa/cosa.