I was just about to post the same question... I am not a Hindi native speaker, but from what I understand, the verb करना means "do," so it seems that an acceptable (or even ideal) translation for this phrase would be as you suggest- "I am doing work."
In this sentence what is the purpose of कर? I thought मैं काम रहा हूँ would be fine in order to say I am working.
When the audio is female..should it not be.. meh kam kar rahi hu, instead of meh kam kar raha hu..?
Yes, I believe you are right. However, I have noticed that on Duolingo, the voices are not consistent in this aspect. On all the other languages also with gendered adjectives, verbs, etc. there is sometimes a male voice that speaks the female versions and a female voice that speaks the male versions.