You are right on this but as this, now that you mentioned it, .docholiday should have at least adressed what would have happened post Seelowe, whether Britain signed a surrender or armistice, this make the whole senario completely differrent, and does Britain retain her armed forces in a reduced capacity, this is never covered.

But many French, Danes, Dutch, Belgians did fight in the East under the command of the Waffen SS.

the main reason why is because Hitler believed Great Britain would become an ally, he didn't want to go to war with them. If Great Britian did become an ally think how different the war would have been, that created the two-front war which defeated the Third Reich. Rudolf Hess knew this, thats why he flew over there to try to make an alliance.

Yes it might have been different. This line of thought requires a much different set of characters in the British government. Even Halifax was unlikely to go any further than a armisitce and eventual peace treaty. An alliance with Germany was beyond the desires of anyone likely to form a government.

As it was the British jailed Hess in isolation and made plans for evacuation of the government to Canada. There were discussions at the highest levels between the British & Roosevelts inner circle about what to do if Britian were to be sucessfully invaded. The evacuation plans included the transfer of British military research and technology to the US. This included the embryonic atomic bomb research the Brits had been collecting.

The assumption of increased difficulties in forming a alliance between the USSR & US do not match the historical events. Roosevelt had long before been establishing connections to the USSR (and made new enemys in the US along the way for that). Were Britian to fall the stratgic sense and pressure to ally with the USSR vs the Japanese and nazis would increase.

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These were but a small number and were considered traitors by their own people and government, consequently they were left with out a country of their own.

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The war against Russia will be such that it cannot be conducted in a knightly fashion. This struggle is one of ideologies and racial differences and will have to be conducted with unprecedented, unmerciful and unrelenting harshness. -Adolf Hitler

Here is something to think about if Germany had invaded Britain.

1, A pro German Puppet Government would be installed.
2, A pro German Monarch would have been installed (if Hitler retains the Monarchy).
3, Britain would more or less retain a cadre defense force (like Vichy France)
4, Britain would under German control would be free to recommence trade with other German occupied countries.

While this might seem fanciful, but could happen.