What mistakes int 'Grand Strategy' led to the German defeats in the Battle of Britain and in Operation Barbarossa?

As historically conceived? No. Barbarossa was built around poor intelligence on the strength of the Soviets, particularly on the scale of their reserves, and wishful thinking based on a campaign plan that had mortgaged Germany's entire future on a war that would be over in 1941 and so made any suggestion of one that might stretch into 1942 and beyond unacceptable.

The poor intelligence dogged the Germans from the start and by August of 1941 it was clear to the Germans that their assessments of Soviet strength had been badly, and systemically, off. The Soviets continued to oppose the German invasion despite losses far greater than German intelligence had predicted they possessed and with troops and equipment that had come as complete surprises to the Germans. For example, pre-war estimates put the Soviet tank park at 10,000 vehicles, less than half its actual total. From the start, the Germans knew their intelligence on Soviet strength contained huge gaps and was constructed largely out of inference. It was also continually being revised upward. In August of 1940, when planning for Barbarossa began, the Germans estimated 170 Soviet divisions opposing their invasion. By February of 1941 this number had crept up to 180, but as pre-attack reconnaissance intensified it ballooned to 226 by the time of the invasion in June, as the Germans continually discovered heretofore unknown enemy formations. This level of new discovery clearly indicated the inadequacy of the intelligence but the Germans took their chances and attacked anyway.

Writing in early August, seven weeks into the invasion, OKH chief Franz Halder noted explicitly how badly they had underestimated the Soviets. Despite this awareness, the Germans continued to accept optimistic assessments that this time the Soviets were on their last legs. In September, they underestimated Soviet reserves before launching Operation Typhoon and then in October they overestimated the effect of the initial (admittedly amazing) success they achieved at Vyazma and Briansk in wiping out another half-a-million Soviet soldiers. This led them to conclude that Moscow was now theirs for the taking, and led to a string of poor decisions. German leaders would subsequently point out that the intelligence in October was telling them the Russians were finished but by then they should have known that such intelligence was based on guesses that had already been shown to be regularly wrong.

One of the reasons for this serial wishful thinking by the Germans was because doing otherwise would be admitting defeat, not just of the 1941 campaign, but for Germany and the entire war. By the summer of 1941 the German Reich, for all its size, was a precarious house of cards. Resources were stretched and the Germans needed a quick victory over the Soviets to allow them to demobilize a large chunk of the army, save on ammunition expenditures, and gain the oil necessary for the following naval and air campaign against the UK and USA (which Hitler considered a belligerent long before the official declaration of war). Even as the Panzers were rolling across the Soviet frontier, production was being shifted away from ammunition and tanks for the army, towards aircraft and ships for the following western conflict. In June of 1941 the Germans mortgaged their future on conquering the Soviets by the end of year. Were that not to happen all the subsequent finely balanced plans would collapse in on themselves and the future of the Reich's entire war effort would be placed in lethal jeopardy. As such the Germans were conditioned to grasp at any straw that seemed to offer the possibility of a victory in 1941, no matter how improbable. This conditioning was so bad that it remained the root of a lot of "if only we did X different, it would have worked" in memoir writing after the war, such as taking Moscow before the end of 1941, and endlessly repeated by pop-historians since.

But let's look at some of these you mentioned treating the Ukrainians and other minorities in the Soviet Union nicer. Well that runs into some problems the Germans had a huge problem with logistics this is a long read but I recommend it if you want to see how bad things were. The Germans needed a quick victory because they simply didn't have the logistics or support to fund a long campaign. They had a huge problem with bottlenecks and supplying their troops one of the ways they got around this was the hunger plan a plan which involved taking Soviet grain and using it to feed German soldiers, the Germans simply didn't have the logistics to feed both their army and the civilian population, yes it dovetailed nicely with the Nazis genocidal aims but the food wasn't their to support both. Could they have treated select minorities better? Maybe and they did do that in caucuses mountains and it could have perhaps been adapted more to other places, but these are smaller populations and you run into the problem of logistics again the Germans had a hard enough time equipping their own troops much less local allies of dubious loyalty.

Then there is taking of Moscow, first when people mention that the Germans were stopped X miles from Moscow it often ignores that one they were stopped and two reaching Moscow doesn't mean you just waltz into the city. Moscow was heavily defended and reaching Moscow is just as likely to be Stalingrad a year early then a war winner. But lets say the Germans do take it, does it hurt the Soviets? Yes Moscow was the hub of the Soviet rail network, the government and a large amount of industry and population. But does it knock the Soviets out? A large portion of industry had been moved across the Urals and while it would hurt the Soviets it does not destroy their war making potential additionally the farther the Germans advance the harder it is to supply there armies and the less power they can bring to bear.

The best case for a "magic bullet" is in my opinion Case Blue going a bit differently it's conceivable that with a less emphasis on Stalingrad more motorized transport being diverted there, plus a lot of luck the Germans might get in range to bomb the oil at Baku taking the majority of the Soviet's oil supply and severely hampering their industry and offensives but first that requires a lot of luck and everything going perfect and second the Germans wanted to capture the oil intact to deal with their own chronic fuel shortages and all this does is get you a stalemate maybe Eastern Europe doesn't fall into the Soviet sphere but the Germans still lose.

That's the gist could battles have gone better yes, were mistakes made yes, but a plan that involves everything going perfectly is not a realistic plan. Maybe maaaaybe the Germans could have beat the Soviets without the US involved and a huge heaping of luck but once it's the US, the Soviets and Britain vs the Axis Germany is doomed and a better plan here or a battle one there is not going to save them.

THE GERMAN CAMPAIGN IN RUSSIA PLANNING AND OPERATIONS (1940-1942)

DEPARTMENT OF THE ARMY WASHINGTON 25, D. C., 22 March 1955 Department of the Army Pamphlet 20-261a i

https://history.army.mil/html/books/104/104-21/cmhPub_104-21.pdf