Italy neutral in WWII?

There was indeed the Anti-Axis coup IOTL, but without an Axis Italy I find it questionable whether it would occur or, if it did, provoke an Axis response. For one, without an active Balkan Front there is no real reason for the Germans to attempt to pressure the Yugoslavs into joining the Axis (Which provoked the coup itself) and, even if they still do, without Italy in the Axis doing such will be much more amendable to Yugoslav interests than IOTL; there's no pressure to allow Italo-German forces to cross through to fight in Greece and, most critically, there is no danger of Berlin applying pressure on Rome's behalf for territorial concessions. IOTL the Yugoslavs were pretty wary of the situation, given the obvious precedent of Germany forcing territorial concessions on behalf of Hungary from Romania while Italian territorial demands were well know. Here, not only are these two threats to the sovereignty of Yugoslavia removed, Belgrade can find a clear benefit in the deal as it could supply resources to the Germans at the premium while achieving security against Italy. 

If they still don't end up joining the Axis or even still the coup, I don't see it as an issue. Yugoslavia won't be opening up a new front against Germany due to the fact the Italians, with their aforementioned demands and not currently fighting in Greece or Libya, will be ready to pounce; as well, the allure of economic gains from trade deals are still there with regards to the Germans. I think the Yugoslavs will realize the moment they prove troublesome to Berlin, Hitler will give Mussolini his full support for an attack and Belgrade knows there is not much the Western Allies can do about it because they don't wish to bring the Italians into the war. Speaking of the Allies, Belgrade will be further deterred from hostile actions given there isn't any Allied troops in Greece. IOTL, they could at least hold to the idea that the British could provide reinforcements to support them, as well as that Thessaloniki would be open to them for resupply purposes. Here, Greece is neutral, Bulgaria is still in the Axis and the Italians control both sides of the Strait of Otranto with their main fleet actually based in the area. Belgrade here will be under no illusions as to the ability of the West to support them.

Now, as to the matter of Army Group South and Operation Barbarossa, allow me to correct myself first as I erroneously said 11th Army when it's actually 12th Army in question. 

With regards to the points you raise with regards to force size, IOTL Army Group Center diverted 3rd Panzer Group to Army Group South which is a comparable force deployment as 12th Army would be. Logistics is also not as much of an issue, as the dual campaigns of Yugoslavia and Greece expended vast amounts of material that had to be replaced. Here, that doesn't occur and instead such supplies are being stockpiled behind the front for the coming invasion. It's also far easier to supply 12th Army on the Ukrainian Steppe, even despite the difference in distances as compared to Yugoslavia, given that Ukraine is largely flat and not mountainous and rail connections are far better. There's also the fact that the detachment of 12th Army combined with the logistical issues of the Balkans Campaign meant Army Group South had a staggered start, while the issue of combat power meant von Rudenstedt had to fight mainly a frontal war punctuated by only occasional penetrations and relatively small encirclements besides Kiev. Here, neither of these causes for this in play, so Army Group South is going to overall have a much better, effective campaign. 

With regards to the effects on Army Group South, IOTL the diversion of 3rd Panzer Group was logistically draining as AGC's supply lines were East-West instead of North-South. A further complication was that the Battle of Kiev was concluded and Guderian's forces attacked for Operation Typhoon in less than a week, leaving no real time to rest, build up more supplies or further plan. Army Group Center also spent most of August wasting resources in fighting around Yelnya due to a desire to maintain a bridgehead to keep Soviet forces more readily pinned in the area while AGC was in a lull. Here, all but Yelnya are definitely solved and, given the Germans did end up abandoning Yelnya anyway in September anyway, I'd imagine they'd never get involved in that quagmire in favor of focusing in on the drive to Moscow. Soviet forces are still in the early stages of building up defenses in the region and reinforcements outside of whats on hand aren't available until November in serious numbers; outside of a few thousand NKVD troops, even as late as October there was nothing to actually fight in the city itself. Indeed, the situation even IOTL as late as October at one point saw Zhukov reduced to less than 100,000 troops in a single defensive line to the West of the City that nearly got cracked open by 2nd SS and 10th Panzer at Borodino; here, however, there is no 32nd Rifle Division arriving literally a day before combat for the Soviets in September. 

To put things into perspective of what the loss of Moscow and Leningrad would mean, I think a review of the material situation is in order. The loss of the Ukraine and other occupied areas engendered shortages of coal (The Donbass was home to roughly 60% of Soviet output by itself), aluminum (Main Soviet facility was along the Dnieper, about 60-80% of production), iron ore (60% of production), steel (50% of production), electric power (30% of output), manganese ore (30% of production), and nickel (30% of production). Overall output of the machinery and metal goods sector had fallen by 40%. In addition, the USSR was also unable to meet the demand for copper, tin, zinc, lead, aluminum, and nickel with remaining sources. Antimony, tungsten, cobalt, vanadium, molybdenum, tin, and magnesium were also almost entirely lacking. Even before the loss of the two major cities in the ATL, as previously cited, overall output decline of the machinery and metal goods sector by 40%; here, the decline is on the order of 80%. The loss of Moscow and Leningrad means that steel, aluminum and nickel have essentially entirely collapsed in production; the loss of Moscow also removes, IIRC, something like a a further 20% of Soviet electrical power given the immense hydro-electric resources in the area. Aircraft production has now collapsed, both due to the lacking of aluminum, steel, nickel and electric power, but also due to the fact that, again, the actual physical elements of production were around Moscow.

As for Leningrad: