I agree with the posts above suggesting that the alliance would not have lasted very long. It was becoming increasingly clear to people by the end of the war that Stalin was easily just as bad as Hitler, if not worse, and that the Soviet Union under Stalin might pose an even more serious threat to the U. S. than Germany had under Hitler, if only because the Soviets were intent on developing an atomic bomb and were using espionage to do so.
Unanswerable question, but I doubt it. The differences in political and economic philosophies and actions between the Soviets and the Western European allies were just too great, and both sides were unable or unwilling to yield to the opposing side. President Roosevelt might have been able to keep things going a little longer since he had a better relationship with Stalin, but I don't think it would have made an appreciable difference.
This is very difficult to say. Certainly FDR was on good terms with Stalin, and the two had made a number of "gentlemen's agreements" at Yalta that were not honored by the Truman Administration. But I tend to agree that the weight of world events and the interests of the two countries would have probably sent events in a similar direction even had FDR lived.
No way to know for sure, but I do not think so. The split up of the alliance was not caused by individuals. Instead, it was caused by ideologies and by the demands of (perceived) national security. FDR could not have changed the basic and very fundamental differences between the US and USSR.