On the other hand, the entire purpose of the Nazi regime was to conquer eastern Europe, enslave or exterminate its population, and resettle Germans there. Victory required a successful invasion of Russia.
Also, few considered air power to be actually capable of fighting battleships until the Battle of Taranto, where the effectiveness of air raids surprised almost everyone. The German planners almost certainly didn't believe in the capability of Luftwaffe to destroy the Royal Navy.
I've never heard that before - do you have any references? The Nazis declared war on America, not the other way round.
The reason USA didn't join outright was that there was serious domestic opposition to the war, and Roosevelt understood well that he needed his Lusitania to be able to bring America fully into the war. The Germans took all pains to avoid this, and USA only managed to declare war after the Pearl Harbor.
In reality, history rarely contains black-and-white narratives where the one side is the clear aggressor. Had the USA not been actively engaging in combat operations against the Germans and the Japanese, they never would have been stupid enough to pick a fight with the Americans.
I firmly believe that the only possible route to German victory would have been capture of Gibraltar soon after the French campaign. German industries sorely needed raw materials, and it's war machine sorely needed oil. The Mediterranean could have provided both, and all the Germans needed to completely secure it would have been the Rock and Suez.
Was the capture of Gibraltar in any way realistic? With Franco joining on the German side, perhaps. The Germans had siege cannons that should have been able to reduce the foundations that Gibraltar stands on into rubble. But Franco had already won his war -- he had little to gain from joining, and a lot to lose.
Without an axis Spain, taking the Rock would essentially have required first attacking Spain. And they had a large, experienced and well-trained army, which would have had good defensive positions on the Pyrenees. I don't know.
It would not have been necessary to actually take Gibraltar -- only to silence it's guns, and place enough artillery west of it to block the strait.