You can say 'I've been studying English.' or 'I'm studying English.' interchangeably. They are both acceptable. 'I've been studying English.' implies that you have been studying it for some unspecified amount of time, while 'I'm studying English' does not give any indication of time. It could mean you are studying English right at that moment, or you've been studying it for a while.
You can use either learn or study. To say 'study' implies you are taking English classes or lessons from a teacher, whereas 'learn' could mean you are learning English on your own, but these are not definite meanings.