No, for a huge number of reasons - not least of which being timing (the cruise missile is in early development now, and these videos are 5+ years old) performance (cruise missiles can't do what the objects in the video did, even if nuclear powered - nuclear power is more an endurance feature anyways) lack of fallout (unshielded directly cooled reactors produce quite a few interesting isotopes) and location (why would the Russians fly a missile like that anywhere near the US?).

No, iirc they've tested two of them and both failed