I was surprised to see the title of this thread when I was viewing the main page of the boards so I had to take a look.
My thoughts on Yoda's exile when taking the Prequels into account is that the power of the dark side which had hid Palpatine's machinations from the Jedi for almost a generation and led to the Clone Wars and the Purge is what led Yoda to his self-imposed exile. He didn't have the power to defeat Palpatine on his own and knew he had to get away at the very least to save himself to help with the future - the training of Luke and Leia. Having felt the deaths of so many other Jedi, yet taking into account the dark influence over the Force at the time, Yoda may very well have believed he and Obi-Wan were the last of the Jedi and being incapable of defeating Palpatine (remember they think at this point Anakin is dead) figure the best course of action is to go into hiding and re-group when the twins are ready for their destiny.
Someone brought up why doesn't Yoda go searching for the survivors of the Purge as Vader was easily able to find them. Keep in mind Vader had the vast resources of a Galactic Empire to hunt down the Jedi. There were Imperial Forces - Stormtroopers, Dark Jedi, Inquisitors, Emperor's Hands, etc - all across the galaxy keeping an eye out for Jedi, this is something Yoda did not have available to him. Assuming he knew there were survivors he may have thought it best not to look for Jedi in the belief that it may help them survive longer. Palpatine and Vader essentially know Yoda survived the Senate Duel so they would be keeping an eye out for him and one would assume he's a big target in the Force (I know doesn't exactly explain why he wasn't found on Dagobah) so Yoda looking for Jedi might not have been the best idea at the time. There's also the technological impact, after hiding away on Dagobah for so long, it's possible that little Wookiee ship he was on would be incapable of flying him across the galaxy in search of Jedi, essentially leaving him stuck on Dagobah until someone (Luke, Leia, or Obi-Wan) came to him.
One of the problems with the Prequels is that it's warped the scope of the Original Trilogy. If you read any of the pre-production work for A New Hope and the other two movies you can tell Lucas initially had different ideas for the time between the Clone Wars and Luke's Jedi training than what the Prequels give us. In the early ideas for Star Wars, the Jedi were wiped out long ago and there had been no survivors for a lot longer than the handful of years we find it out to be thanks to the Prequels and EU. So Yoda being in hiding is much easier to explain since it can be assumed that there have been no Jedi for 40, 50, 100 years. But the events of the Prequels change that and thus we have to change our viewpoint on the actions of Yoda and Obi-Wan. I think we find that their actions are made out of a belief that they (and perhaps any Jedi survivors, whether or not they are known) are incapable of stopping Palpatine and as mentioned that only Luke and Leia can do it. But if they do anything before the twins are ready to take on their destiny they risk the chance of destroying their only hope - which would be why Obi-Wan doesn't attempt to train Luke - sidebar on that point when isolating ANH on it's own and from a storytelling pov, Luke can't be trained until a personal trauma (the death of his family) leads him down the path of abandoning his current way of life to follow his destiny.
Oh and as far as how long the events of ESB take, I always felt it was a couple of months. As mentioned, the Falcon did not have a fully functional hyperdrive after they escaped the Imperial fleet so on sub-light and assuming their current position was less than one light year from Bespin, this timeframe could be months. Also there's a lot of training for Luke to do, despite his affinity for the Force I highly doubt he could learn all he did in just a few days. From a storytelling pov that's not believable, which yes I know is saying a lot when you take into account some of Lucas' work in the Prequels. As for Han and Leia's clothing, my guess would be they shared some of Han's clothes on the Falcon (he should have some sort of laundry unit on the ship) and that when they got to Bespin any additional clothes they received were either gifts from Lando or bought with any money they had or perhaps earned (Han could have always won a few hands at Sabacc).
Ok so that was a lot, you can see I think an awful lot on this kind of stuff - 30+ years of viewing the movies and reading the EU gives the opportunity to expand what we think and know from Star Wars to fit it into our own liking. This is how I personally can fit much of the EU into the Saga and resolve conflicts like the various timelines created by the comics between ANH and ESB (Marvel, Sunday Comics, Dark Horse) and that's what is best about Star Wars. Regardless of what Lucas has written, especially with the Prequels in contradiction to the Original Trilogy, we as the audience can decide what has truly happened at least for us individually.