That change could easily spin off in several directions.
[*]FDR was a high-energy, driven, and intelligent member of one of the most famous and well-connected political clans in US history, so with no polio, probably enhances his political pursuits (1)
1)
Its just difficult to tell what happens. An earlier entry into US presidential politics could thrust him into the Dem nomination for 1928, which was an unwinnable one, even for FDR. Though he might have been wise enough to wait until the time was ripe. Unfortunately, in the American republican system, no matter how much one party turns things to poo as of Election Day D+1 1928, the Dems don't have a chance to swear in their own guy as POTUS until 50 months later in 1933
No Votes of No Confidence over here. Though don't bother trying to tell the Vast Right Conspiracy
[size=-2]tm[/size] and the Tea Party.
[*]Historically, he went to great pains (literally and metaphorically) to limit the public view of his paralysis. I can't help believe the physical stress contributed to the deterioration of his health. (2)
2)
Things got so bad for him at the end that he was forced to apologize to a joint session of Congress (and nationally via radio and newsreel) that the ten pounds of steel he was forced to carry didn't allow him to stand anymore.
Perhaps he not only lives through the end of the war, but is also more vitalized the last couple of years. (3)
3) He smoked like a chimney, drank not heavily but a lot, and worked as POTUS in the most exhausting era ever for a president short of the ACW. Plus he did it 4 years and 87 days longer than any other POTUS. He also lacked any sense of his own mortality. He spoke of running for UN Secretary General after he left office in 1948. He may be in better shape, but not a whole lot better shape.
AISI, his biggest problem was his rose-colored glasses POV regarding the Soviets. I don't think that's going to change just because his physical strength is far better. Maybe it makes for a better Yalta and Potsdam, but IDK. After Yalta, Potsdam really needed someone like Harry S. Truman to tell Josef Stalin to "Go to Hell". ITTL, Potsdam could well turn into Yalta 2.0
What does that mean for the post-war? (4)
4) Harder to deal with the Soviets, more mischief making by Stalin. At least Truman, as the newbie, was willing to listen. FDR's style was far more "vertical".
[*]In large part because of the travel difficulties and that desire to avoid being seen in public in the wheel chair, Eleanor made many visits across the world to do the face-to-face meeting with normal citizens, soldiers, and sailors. (5)
5)
Eleanor had the stamina of an African bull elephant in full charge. She was making all those visits because she wanted to, and because she had nothing to look forward to at home (regardless of FDR's handicap). FDR used her because she was enormously popular outside of White Dixiecrats, because she could make promises that FDR may or may not have intended to fulfill, and to take advantage of her own considerable political skills.
She became the moral conscience of the President. (6)
6)
FDR needed that too. He was seen even by his friends as "too much the politician". Eleanor gave his administration of earnestness that otherwise it would have lacked.
If FDR is physically able to do more of those trips, does he go? (7)
7)
Hard to say. The USA was transitioning from a time where some people had radios to everyone having one. So the need to do whistle-stop tours were not as necessary. But I'd say, yes, he would. Truman did in 1948, when Dewey did not, and it killed Dewey.
If so, how does that impact social programs? (8)
8)

The enemies of those social programs were a prostrate Republiucan Party, and the out-of-control Charles Evans Hughes Supreme Court, which just the threat of passing FDR's Court Packing Bill was enough to break them.
Or, does Eleanor go on those visits anyway? (9)
9) Yes, she secured the African-American Vote through to the present day (kudos to the Earl Warren SCOTUS, JFK, and LBJ too).
[*]Does FDR make a presidential trip to Britain? (10)
10) No

Not unless he's healthy and its post-VJ Day.
He stopped at various British island in the Caribbean and of course the Atlantic Charter summit done aboard the warships off Newfoundland. (11)
11)
Sailing about the high seas thousands of miles out of range from the Luftwaffe, aboard battleships, and surrounded by flotillas of escorts, is not the same thing as trying to penetrate U-Boat wolf packs, facing Luftwaffe air raids, V-1 buzz bombs, and impossible to defend against V-2 rockets. To be blunt, had Churchill been lost to an unexploded bomb while touring London during the Blitz, he could have been constitutionally replaced within days by a Parliament that could have quickly chosen the BEST possible candidate for a wartime Prime Minister leading a National Government. Bevin, frex.
But let a V-2 land on FDR's head, and you have Henry A. Wallace as POTUS. A guy whose glasses facing the Soviets were not rose-tinted, but almost cherry red! It would be many years before the scales were removed from Wallace's eyes. 1942-1944 were not those years.
The US President has far more power and responsibility in his office than does a British Prime Minister. He leaves a helluva void when tragedy strikes. Big advantage to the parliamentary system is that when its time for the PM to go, there's generally a good choice of candidates to choose from for a replacement.
He also entertained both the King and Churchill on several occasions in the US, but never a formal and very public visit to the UK. (12)
12)
Not the same thing.
As an example, when Churchill sailed to the USA he reached a land (CONUS) that was free of any threat of attack. He was greeted almost as a national hero (half-American, you know), a standing ovation as he became the first foreign leader to address a joint session of Congress, and more to the point, FDR invited Churchill to perform the annual lighting of the White House Christmas Tree. Meaning, it was so safe that blackout conditions weren't needed. Things were THAT safe. Until the U-Boats showed up.
