live vs living

You can ask either question, they are both acceptable in English.

I have noticed, though, that many speakers of foreign languages are more likely to make errors in English by using the present participle (i.e., living, talking, reading, etc.)--something which English speakers seem to rely on less than is the case in other languages.

Either is correct but for me 'living' has a less permanent feel to it so I might use it for someone who I knew didn't currently have a long term address
eg
A: We've just moved to Sydney and I'm looking for a house in the eastern suburbs.
B: Oh good luck. Where are you living at the moment?

"Where do you live?" is the most common. But, "where are you living?" fits just as well. But that is often used after a person asks you first I.e
"Where do you live?" person A
"I live....." you
"Ok." person A
"Where are you currently living?" You.
But as you see it seems more proper than a simple where do you live.

MonaL nailed it.

The present simple, in situations like this, denotes the routine, the habitual, the normal, the all the time. That's why "living" has less of a permanent feel to it. It usually denotes short time actions, centered around the present.