'Do you live in Moscow?' is correct.
You should use present simple because you are asking about a 'habitual' action.
You could say, 'Are you livING in Moscow?', but this has a slightly different meaning (you would be asking if the situation has changed recently, or if it is only temporary).
With present continuous, the verb following 'be' is always in the __ing form.
Compare this to adjectives:
Are you happy?
Are you Russian?