Re: World War II invasion of America:
Despite the IJN's enthusiasm for an ambitious invasion of Australia on the back of the stunning victories in the first few months of the Pacific War, and ignoring the various inter-service rivalries between the IJA and IJN regarding the IJA's conquests in China and the the absence of IJN conquests elsewhere and the benefits accruing to the respective services from such conquests, it was agreed at IJA/IJN conferences and Imperial Conference in February/March 1942 that it was beyond Japan's capacity to invade Australia (with a population of about 6 million at the time and a vast coastline and internal acreage which it lacked the manpower to defend against the sort of assault Japan launched on the Philippines).
By the beginning of 1943 it was apparent from the Japanese defeats on Guadalcanal and in Papua that Japan was on the back foot even in its thrust towards Australia.
Among the reasons for those defeats were the inability of the Japanese to deploy sufficient troops and shipping to support the troops, which was a consequence of Japan's involvement in China and the size of its merchant fleet when it went to war. All of that just got worse as the war progressed.
There was no way that Japan could have mounted an invasion of the west coast of the United States of America which had the slightest hope of success, never mind an invasion which could have forced America to surrender, for the same reasons that Japan couldn't invade Australia but magnified by the problems of crossing the huge Pacific Ocean without the advantages of the island chain and distances involved in the conquests down to Papua and Guadalcanal by mid-1942.
There is also no way that Japan could have mounted any useful land invasion of the USA when Japan was at its zenith in the first half of 1942 as it couldn't even manage to displace a relatively small force of Americans on Guadalcanal a quarter of a planet away from both America and Japan and long before America had got itself onto anything like a full war economy that made a major industrial and military contribution to the defeat of Japan and Germany. That does not detract from the sacrifices on and critical importance of Guadalcanal in turning back the Japanese tide on land and sea at a psychological moment in the face of unstoppable Japanese advances to that point, but the forces Japan and America were able to bring to bear against each other on Guadalcanal were nothing like the superiority America could have brought against Japan on mainland America.
None of that alters the entirely reasonable apprehensions of people in Australia and America in the first couple of years of the war that Japan seemed capable of invading both continents. But historical facts show that there was no prospect of it succeeding in America, and at best a very modest prospect of it succeeding in Australia. At least as long as the Australian government maintained its spine and didn't give in until Japan was in full control, which was most unlikely to happen with modestly vigorous and sustained Australian defence of its land.
As for not invading America because most Americans were armed with 'guns', I'd need to see some figures on gun ownership in the western states of the US, primarily California, which supports that even if it was the Japanese view. The guns the Japanese needed to be afraid of were the USN and US Army guns, and many more military rifles with attached soldiers moved to that theatre, available to defend the west coast and, perhaps more importantly in wearing down an enemy with vastly overstretched supply lines, the interior as the invader advanced.
A rational army would run away.