Is it permissible for a girl to live in the same apartment with a young man who is a stranger to her, even if his room is separate and she does not meet him, and they share a kitchen with two separate doors?

The presence of a foreign girl and a foreign young man alone in a single apartment is a cause for fitna (temptation/discord). Scholars have stipulated, for the permissibility of a man cohabiting with foreign women, that there should be no shared facilities such as the kitchen or bathroom. If they are shared, then cohabitation becomes forbidden. Since the main door and kitchen are shared between you and the young man, it is obligatory to cease this cohabitation if possible. If it is not feasible, then necessities permit prohibitions, and one of you (girls) should reside with the other.