France
German..
The Western Allies should invade France.
They were Allies. But nearing the end when the Italians wanted to kick Mussolini out of power, Hitler sent in German troops to take control. He didn't want to lose the country, so he sent in his soldiers temporarily to fight the Allies and make sure Italy stayed its ally. But he didn't invade it in the way that he invaded other countries such as France.
The Allies did not invade New Guinea. They protected it from the Japanese invasion that began in 1942.
The Allies never invaded North America. They did invade North Africa with Operation Torch in November 1942.
At the time, Nazi Germany was pressing hard against the Soviet Union on the USSR's west. It would not be unreasonable to believe that Stalin wanted the Allies to invade Western Europe as a way of drawing off German troops, etc.
June 6, 1944
Normandy, France.
Operation Overlord
No, the Allies never had any intention to invade Manchuria.
Hitler invaded these countries because he needed allies, but in general public he said that he was invading these places for German citizens to live.