A demonym is a noun that specifically refers to a person from a particular location; you can’t use it as an adjective.

So in your second list, a school can’t be a Muscovite, since it isn’t a person. You could have met a Muscovite at the school in Moscow.

You would just say that you dated a Londoner. You would then use an adjective to describe the Londoner further (a female Londoner) or make the sentence longer and a bit clunkier IMO (a Londoner who was a woman)