If you are talking about the buildings within a city, then it's fine, but spelt differently. "This city's buildings are beautiful".

Well, this depends. Are you referring to multiple cities? If you are, for example, referring to buildings in San Francisco, London, and Paris then you might say "When looking at these cities' buildings you may see a variety of styles." If you are actually referring to the buildings in a single city you might say " this city's buildings are beautiful." But if you are referring to buildings in cities in general you might say "city buildings vary in size and shape." That last one is less specific to a city or the buildings.

No, you would normally use a compound noun: "city buildings".