“I work” vs “I am working” / “I live” vs “I am living”?

I just watched two IELTS speaking videos. The first one’s result is 8.5-9.0 and the second one’s result is 9.0.

IELTS speaking Band Score 8.5-9.0: https://www.youtube.com/watch?v=wzzOowpCryw

IELTS speaking Band Score 9.0: https://www.youtube.com/watch?v=HjrlnyFKVKU

In the first video, there is this simple question:

A: ...Do you work or study?
B: I am still studying in my final year

In the second video, there is more or less the same kind of question:

A: ...Where do you live in your country?
B: I live in Hyderabad....

I asked my two British native friends. One said it should be “I am working” or “I am living”, but the other one said both of those are fine.

So my question is which one is better to answer such question?

• “I work” vs “I am working” ?
• “I live” vs “I am living” ?