[Mary started learning the piano when she was five and is still carrying on.]
1. Mary has been learning to play the piano since she was five. She is sitting the grade 3 examination in the coming autumn.
2. Mary has been learning to play the piano since September, 2011. She is sitting the grade 3 examination in the coming autumn.
I wonder if sentence 1 and 2 are correct?
(Not a Teacher)
They both sound fine to me. 'The' is not strictly necessary in these sentences. Also, I don't think you need a comma between 'September' and '2011', but I'm not certain on that point.
And do delete the comma after September.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.