As for where the Nazis get north American land...
If we posit the "Lightning in the Night" scenario (the only even vaguely serious Nazi's Invade America book I'm aware of...and even it is a tom-clancy-esque propaganda piece).
In that June, 1940 book, England surrenders on Sept 17, 1940, including its navy, after Nazi's (repeatedy?) use chemical weapons on London, killing tens, maybe hundreds of thousands, including the Royal Family as several MPs. The headline in the book is "Brits surrender Navy to save civilian lives!" (My assumption is the use of chemical weapons...not much else might get britain to surrender. If only because it's easier to deliver chemical weapon to london from calais than it is to get them to germany from kent)
Part of the peace treaty includes signing over several colonies in Africa and the Americas from Britain, Holland, Denmark, and France to the Germans: Jamaica, British Guyana, Tanzania, Rhodesia (again German East Africa), French West Africa, Greenland, Iceland, the Falklands, British Virgin Islands, etc.
When the Monroe Doctrine is suggested, Germany states 'these aren't new colonies, they've just changed ownership.' and with help from strongly isolationist sentiment, the US government buys it. British Guyana and Jamaica are excellent places to start influencing paces like Venezuela and Brazil.