it is also correct to say "my girlfriend is living on this street" or "my girl is living on this street"
I would say yes. "живёт" can mean "lives" and "is living" because Russian makes no distinction between the simple present and the present continuous.
It can mean either, but the first assumption would be that she lives in a house on the street.
Duolingo uses American English. The common British usage (I think) "she lives in this street" would have, in American English, the implication of homelessness.