I'm not sure if this could be a general question or a what if scenario... When it comes to the second front, we all know Russia wanted the Western Allies to attack Germany head on through France, as they had political aims in mind just as much as military goals. The British like the idea of attacking from the South and possibly through the Balkans and driving up to Germany. This approach also had political motives. The US favored the direct attack on France to drive the Germans back to Germany. The British felt they could sway Western Democratic influence far into the South and East of Europe, in essence cutting off the Russian line by getting there first, and lessening the "iron curtain." Stalin wanted to keep the Western Allies as far away from Eastern Europe as he could, to increase his influence. Now if the British won the argument against both the US and USSR, and the Western Allies decided to use the Southern/Balkans/Mediterranean offensive strategy and invade through Greece/Balkans and it was successful in gaining a foothold that would lead to a hard drive up through Southern Europe into Germany, thereby increasing Western influence to the East, cutting off the Russian advance, etc., would the Russians have still fought against this because of political motives even though the Allies succeeded in opening a second front and successfully began fighting the Germans in numbers to lessen the load on Russia? This could have lessened friction between the two Allies, as well as eased the Cold war in the post-war world, but would this have been something Russian would have been fine with, having Western military success close to home? And yes the Russians bore the brunt of ground fighting in the war, but every time the Allies made a major landing or an assault from late 1942 onward, the fighting on the Eastern front seemed to tip into the Russians favor more and more, from Torch to Husky through Overlord, I believe those offensives played a major role in lessening the German fighting load in the East just as much as the bomber offensive.
It was possible it would stay out of the what-if realm, but most likely it wouldn't. Still could be a interesting debate though.
I'm afraid the British "winning" the argument and convincing the allies to open up a front from the South is simply a none started. Stalin would have never approved of this and when Churchill hinted at such at Yalta Roosevelt immediately knew. Like it or not at that time, when Stalin spoke all others listened not the other way around. Stalin's word was final.
Really? Why would they need Stalin's approval? Indeed they wouldn't need to inform him much in advance of the fact. When was he informed about the invasion of France, Sicily, or Italy?
Is this a serious question? These countries were allies. Communication existed. At Yalta, Churchill wanted to open up the second front from the south (Balkans area) to prevent Soviet Union from swallowing up Eastern Europe. It didnt happen only because Stalin said no. Nothing at Yalta would be done without Stalin's approval this is not to claim that Stalin wasnt going to do the same. Allies work together but the Red Army made many nervous.
They were indeed allies but that doesn't mean that independent operations were approved by everyone. Which Soviet operations were approved by the British or Americans? The operations in the Balkans didn't happen not only because of Stalin's opposition or arguably even primarily because of his operations. The US and indeed many of the British didn't consider landings there the best way to end the war and that was the primary goal.
The decision to move south instead of north was finalized in a series of conferences ending in July 1941 with the advance into the 南方資源地帯 (Nampo shigen chitai or "The Southern Resources Area") being agreed upon.
Everything that occurred after Yalta was agreed upon by all parties. While individual operations didnt require approval (no need) such as Operation Market Garden or Bagration overall goals were agreed upon. Italy would be liberated by the allies for example. Poland was Soviet.... Common sense prevailed of course. Stalin wasnt going beyond Berlin and the allies werent going in it. Capture of Berlin by the Soviets was agreed upon by the British and Americans. Increasing pressure on the Eastern front in order to relieve some from the Western during the Ardennes Offensive was also agreed upon.
And completely irrelevant. By the time of the Yalta conference there wasn't going to be a Balkan invasion by the Western Allies. There simply wasn't time for it. Prior to that the decision not to go to the Balkans was made by US and British planners and I've seen nothing to indicate that Stalin had any significant impact on that decision. As for the capture of Berlin that was pretty much a forgone conclusion at that point given the distribution of forces. Certainly Stalin wouldn't have listened if the British and/or the US had tried to veto his taking the city and the US had already decided pretty much unilaterally not to try and beat the Soviets to Berlin. So that hardly supports your position and indeed is only marginally relevant to it. The allies did ask each other for help including timing offensives but that doesn't mean that they had much less exercised a veto power over each others operations. Also please note that your first sentence is contradicted by your second. No where near everything that occurred was agreed upon by the three parties much less all parties.