Dear Biah,
You wrote " I am studying english since 2009". This sentence is fine except for the addition of "since 2009". So you can say "I am studying English" meaning that you are studying now or for what you mean that you 'study English' as a continuous action as in "I am reading this great book" whilst you may not be reading in at that moment in time but you are in the process of still reading it.
You further wrote ''I have studied since 2009'' . The correction given above by Jura seems to be the most correct.