In the case of the street (Pushkin Street), yes, you need to capitalize it. If you want to say "Moscow City," then yes, you should capitalize both words. But normally we don't add the word "city" to the name of a city, unless it is actually part of the city's actual name. For example, "Oklahoma City" is the name of a city in the state of Oklahoma. You have to call it "Oklahoma City," not just "Oklahoma," or people will think you mean the state. But for most cities, we just say the name of the city, by itself, without the word "city" at the end. For example, "Phoenix" is the name of a city. We don't say "Phoenix City." We just say "Phoenix." If we need to clarify that it is a city, we say "the city of Phoenix." The same is true for Moscow. We just call it "Moscow," or "the city of Moscow," not Moscow City.

H Elena, yes, those words should have capital letters, they count as proper nouns.

Gray gave an excellent answer. “Street” is capitalized and “city” and “town” aren’t normally used.

Elena hi. Message me for English practice