In my knowledge, it is typically assumed that a victorious Fatherland-like Nazi Empire would have have been doomed to fall the same way as the Soviet bloc in the very long term.
I wonder, could they have avoided this fate by adopting the same policies that China has (so far) successfully adopted ? I.e. scrapping lousy Nazi education policies and re-fostering sound academic excellence, economic liberalization, greately lessening the ideological burden and interference of the state in the everyday life of the apolitical majority as long as they give loose passive loyalty to the regime, fostering consumerism (and welfare) to keep the citizens content, redefining the regime's ideology away from strict (and increasingly laughable as modern biology progresses) Nazi racist anti-Semite and anti-Slav dogma towards Pan-European nationalism (although I can see them quite successfully fostering racist hostility towards say Muslims to the present day).
They would still likely have a technology and economic gap vs. the United States, but if they liberalize the economy and re-foster sound education policies it needs not be nowhere as severe as the one the USSR accumulated. By itself, fascism is typically rather more economically efficient than communism.
Concerning the (foolhardy) scheme to implement US-style population substitution colonization of the whole European Russia, I have severe doubts that the mass expulsion or extermination of its native Slav population would not break the back of the Nazi Empire's economy. As such, I assume that the regime would necessarily give up such efforts as futile. Likewise, trying to implement total military control of the whole area against Slav guerrilla would be quite burdensome. However, I doubt that an empire that can freely tap the economic and manpower resources of whole continental Europe would have serious troubles sustaining endless low-intensity conventional war on the Urals border. Even with covert US-UK support, such Russian efforts would be relatively pitiful, since a rump Russia that can only draw on the resources and manpower of Siberia and Central Asia would be pathetic in comparison to Nazi Europe (unless the Nazis effectively expel most of the European Slavs beyond the Urals). Widespread guerrilla in European Russia itself would be far more troubling. But even so, if they re-aim their counterinsurrection policies from trying to hold everyting, to garrisoning only the heavily colonized areas and the ones with valuable natural resources, periodically bomb and raid the rest, and implement colonization in a staged, territorially continous way from Poland, they may have a chance.
Although I am persuaded that they may have much better chances of successfully establishing their Lebenstraum if they implement it in Africa than in Russia, for various reasons (e.g. natives would be less capable of organized resistance, would draw less help and sympathy from the rest of the world).
Another issue that would threaten the long-term stability of the regime would be the upcoming political an social rebelliousness of the baby-boomers and Gen-X at home. Quite possbily, the regime would have to face a Tienanmen situation or two. On the other hand, if the regime can survive the initial onslaught and successfuly implement economic prosperity in the long term, China's example indicates that consumerism can keep even the majority of the new generations passively quiet and content.