In particular, when Churchill flew to Moscow in August 1942, did his plane fly over German occupied Russia, or did it just take the long route through the Arctic?
No. In fact, BOAC Flight 777 (a civilian flight) flying from Lisbon to Bristol was shot down by the Germans. The predominant theory for the reason the plane was shot down was that the Germans thought Churchill was on board. Of course, that wasn't the case. Instead, the actor Leslie Howard, who acted in Gone With the Wind, was on-board along with several other passengers and crew.
Molotov's 1942 flight to the US crossed over the front lines in a converted Pe-8 four-engined bomber. It traveled over the Baltic and made refueling stops in Scotland, Canada, and the US. The flight evaded enemy patrols, but was attacked twice on the return leg by both German and Soviet fighters without sustaining damage.
Source
Rzheshevskiĭ, Oleg Aleksandrovich. War and diplomacy: the making of the Grand Alliance ; documents from Stalin's archives edited with a commentary. Australia: Harwood Academic, 1996.