I have simple example of NFA->DFA conversion, but I am confused about "q0,q1,q2" state. What is it for? Or maybe I have done something wrong?
Yes, it seems you have done the transformation correctly.
But a correct result is not automatically the most efficient one. You could add "b" to the loop of state {q0, q2} and just delete the state {q0,q1,q2} with all the transitions that touch it. Both DFA accept the desired language.