I think they're used a bit more abstractly in this context, especially since it sounds like an article related to art.
Interrogate may be being used in the sense of "asking questions of". Perhaps something like looking at the art in the city and using it to determine the culture of the city and the people there, and the kind of things they are trying to express. Interrogate might be being used instead of investigate in order to emphasize the thoroughness of this inquiry.
I think in this sense negotiate might mean trying to find, change, or establish your place in the city, in the sense of making a name for yourself and/or finding where you fit in to the life and culture there.
In my experience, articles written about art, and authored by artistically minded folks, tend to use more abstract meanings of words that are hard to nail down to a concise definition. They seem to rely more heavily on context and the reader's familiarity with the art world and the tendencies of the people in it.