Could this mean eating an unspecified amount of banana? If so is "i am eating banana" also ok as translation?
That would be correct. "I'm eating a banana" should rather be translated *"syön banaanin" in Finnish.
Why not simply "Syön banaani"?
Banaani is the form used when it is the subject of the sentence. Here it is the object, so it is either banaanin (ackusative) or banaania (partitive).
Yes it could. If "I am eating banana" is grammatically correct in English, it should be accepted.