1. New York City is in USA.
2. New York City is in the USA.
3. He lives in New York City, USA.
4. He lives in New York City, the USA.
=============
Q1: Do we have to use 'the' or not?
Q2: Can we use "New York" instead of "New York City"?
2 is better than 1.
3 and 4 are both acceptable.
It's best to use New York City because New York is a state.