The British Blockade on Germany was definitely one of the most important factors of the war, and if it would had been possible for Germany to avoid it, then their chances of victory would had been far greater. But unfortunately for Hitler, the United Kingdom is defended by the Greatest trench ever built; The English Channel, and objectively looking at it… It’s almost impossible to imagine a situation where Germany successfully managed to knock Britain out of the war.
As long as the Royal Navy was still afloat, the United Kingdom was more or less impervious to any German invasion, and without the serious threat of a German invasion, the UK had very little reason to seriously fear an invasion.
In North Africa… As you alluded to, I doubt that sending more divisions would had ended up positively impacting the DAK’s performance. The Italians couldn’t even supply the initial two German divisions in Norh Africa even before Rommel went on the offensive. Adding more divisions might have made the Germans perform better, but I suspect that if the OKH sent 7 divisions, they would had all ended up collecting sand in the desert because there was no fuel to run them with.
It’s a bit of a paradoxical Catch-22: Germany needed oil to be able to win battles, but needed to win battles to get that oil.
I would echo Spartacus in the conclusion that
I suppose that if we really tried, we could probably think of some insane scenario where Germany managed to lure the Royal Navy into a trap and beat them and them with some magical invention invade the UK, but at that point, we’re just turning into the History Channel with conjectural alternate history.
Germany, indeed, was just throwing Hail Mary’s, it was their entire strategy. They went all in over and over and over, gambled everything on chance, it was bound to fail sooner or later.
During the Polish campaign, they gambled everything on that the French wouldn’t seriously pursue the Saar offensive. During the French campaign, they gambled everything on the Ardennes push. During Operation Barbarossa, they gambled everything on success within 2-3 months.
And just like with any gambler - Sooner or later, you lose everything.