Very, very nice!
In the last set there was the State Historical Museum building (red brick) that you'd visited earlier. This was built on the original site of the first building of Moscow State University and opened as a museum in 1894. It was dedicated to the then-recent coronation of Tsar Aleksander III. I'm glad that you posted those beautiful photos as more visitors to Moscow should make this a part of their Red Square experience.
Address: 1, Red Square, Moscow (lots of folk take photos of the address sign on the corner of the building.)
Metro stations: Okhotny Ryad, Ploshad Revolutsii, Teatralnaya Ploshad.
For readers interested in the buildings on Red Square: in that last photo set was a brightly coloured church. It is at the entry to Red Square, offset behind the State Historical Museum and just across the side street of the GYM (Ghoom) shopping Centre. That is the Kazan Cathedral; not a regular "working church" but open daily for tours and one can light candles and pray. It was torn down on orders of Stalin but rebuilt in 1993. It was constructed at the end of the "Time of Troubles" and dedicated to the Kazan Icon of the Mother of God which was carried by the liberators and credited for helping expel the foreign invaders. Later it's Archpriest would assume leadership of the "Old Believers."
The side street separating the Kazan Cathedral and GYM is Nikolskaya Street, so named because it leads from Lubyanka Square (KGB) to the entrance of the Kremlin's Nicholas Tower. These days it is a pedestrian-only street and filled with small shops and mostly gourmet cafes. In 2013 Russia's first Krispy Kreme donuts opened to lines of youth who waited for hours but Krispy Kreme was ready for them with entertainment and free logo items.
You showed the ancient remaining portion of the walls to Katai-Gorod (China town) at Zaryadye, built in the 1500s, and the city has approved a full restoration to prevent further deterioration. Nikolskaya Street connects these to Red Square. There is still vehicular traffic along the walls but that street will be converted to pedestrian-only just as Nikolskaya was converted in 2012/2013.
Trivia: the beautiful Iberian (Resurrection Gates) main entrance to Red Square was in ancient times a part of that Katai-Gorod wall:
The red brick building to the right here is the State Historical Museum from Mr. Mann's tour. The building to the left is known as the old Moscow City Hall.