Those are all pretty substantial questions; as a starter for ten, a couple of my previous answers cover (3) (it was aircraft, rather than tanks, that were towed over the border): [Did america give planes to britain in 1940 by leaving them 1 mile from the Canadian border?] (https://www.reddit.com/r/AskHistorians/comments/7oar9z/did_america_give_planes_to_britain_in_1940_by/ds8b01g/)

And (to an extent) (4), the relationship between Britain and the US in 1940: [In Churchill's famous "We shall fight on the beaches" speech, he mentions the New World, "with all its power and might." What was the Europe's perception of the United States in the early stages of World War II?] (https://www.reddit.com/r/AskHistorians/comments/84issz/in_churchills_famous_we_shall_fight_on_the/dvqic25/)

(6) and (7) are touched on by /u/Subs-man in [Why did the 1945 UK general election go the way that it did?] (https://www.reddit.com/r/AskHistorians/comments/59kei7/why_did_the_1945_uk_general_election_go_the_way/) - the war-weary British public looked towards social improvements promised more firmly by Labour, particularly represented by the Beveridge Report of 1942; see Paul Addison's The Road To 1945: British Politics and the Second World War for a more complete view of the shift in politics over the war.

It might be worth making separate posts if you'd like more detail on any of the above or the other questions.

I will take a crack at questions 1, and 5.

While both of these questions are pretty much answered in the movie itself, I want to provide two things in answering both of these questions. 1. Broader context (you'll notice from my answers here that I love to broaden context, but that is because humans are complex entities, and having someone pigeon holed is rarely useful), and 2. sources outside of the movie.

As for your first question: "Why did king George have such a dislike for Winston Churchill" This can be rolled into so many other rabbit holes, including delving into your fifth question. But Winston was a very divisive person at the time. It would be a mistake to use the benefit of hindsight to place the reputation the Churchill enjoys today with the one he had at the outset of WWII.

You see Churchill had many prior political posts, finally culminating in becoming Prime Minister of the United Kingdom. His first ministerial position was that of the President of the Board of Trade, a post which he held from 1908, until 1910. He had 10 other ministerial positions (notwithstanding being leader of the Conservative party, and Minister of Defense - while he concurrently held the title of Prime Minister), his last ministerial position before taking on the PM's office, was First Lord of the Admiralty. All of these positions were available only to Members of Parliament, which he made his first attempt at running for in 1899, winning his first election in 1900. While wikipedia is generally frowned upon as a source, this background is merely just a backdrop for the subsequent material here, so for this, I solely used Churchill's page.

While Churchill was certainly intelligent and full of wit, this is not however, what made him divisive. The two biggest things that effectively made Churchill a backbencher were his implementation of the Gallipoli campaign in WWI, and him being seen at the time of Chamberlain's resignation as a war hawk, with a war weary Britain.

Churchill would forever be haunted by the Gallipoli campaign in WWI. The Gallipoli campaign was designed to open up a new front with the 'Sick Man of Europe', the Ottoman Empire. This attempt at opening up a new front would result in almost 500,000 casualties on both sides in about a 9 month period. This was a clear example of a civilian politician implementing his own views in place of military experts. Source. This leads to the second point of him being seen as a war hawk. He regretted immensely and learned heavily from his Gallipoli experiences, which would serve him well in WWII.

His demonstrated propensity to discard expert advice, even when so many lives were on the line, concerned many, especially on the brink of a new war. You see, at the time of Churchill's investiture as PM, many at the time were in Neville Chamberlain's camp. This was in large part due to the war weary outlook of the nation as previously discussed. Hitler was also a master schmoozer, his initial tactics of appeasement started out small. It started off as - 'the Versailles treaty has so strapped our nation that we cannot function, let alone pay for war reparations.' This caught the eye of many European leaders at the time, because they certainly had an interest in at least getting their payments from Germany; so the leaders eased up on Germany. Then came the military buildup, under the guise of wars have changed and the threat of outside influence (read: communists) could irrevocably change Germany. Again there was an invested interest in 'saving Germany from the communists,' and after all, the art of war had intact changed, so easing on military restrictions was allowed. Then there were territorial takings such as the merger with Austria, Czechoslovakia, and Poland... It is interesting how at least in popular historic discussions, the Czech takeover is just mentioned as just that a unilateral takeover, without consent of anyone. But as many here will know, that isn't true. Chamberlain effectively sacrificed the Czechs to the Germans in order to avoid another war. Many in power, including the king, believed that just one more concession would finally end the prospect of another war. Churchill was the antithesis of this entire concessionist outlook. He believed Hitler to be a thug, holding Europe for ransom, until he would finally have the continent, and eventually Britain.

Both these things made Churchill unpopular, or at least, a wildcard from the traditional deliberative process the Parliament was used to, this made the King have a sour taste in his mouth at the mention of Churchill because he knew what he had done, and knew what he was now wanting to do. A slightly more peripheral reason is also that Churchill flipped parties more than once in his political career. Source, by R.J.Q. Adams, a British History Expert.

As for your fifth question: "What was Churchill's role before PM? Why was he the next choice for Prime Minister when clearly Chamberlain, the king, and so many others thought he was a constant failure from previous battles?"

Assuming that you aren't British, it is important to note that The British system of government is in a lot of ways very different from the American system. The two most important differences for this question are that elections can be called by the PM at any point in a Parliamentary Session, and that the PM can resign and be replaced by the majority with one of their own.

Chamberlain's main efforts as PM were to stave off another war. It was the bulk of his platform. When Chamberlain left Germany for the last time, and returned, proclaiming that he "believe[d] it is peace for our time." He started to back himself into a political corner, as his trusted Hitler's promises. When Germany invaded Poland in September of 1939, Chamberlain issued an ultimatum, if Germany wouldn't withdraw their troops, Britain would carry out its obligations with Poland (war). The Germans never withdrew, and the political scene after the deadline passed caused Chamberlain's ability to lead to be in doubt. Instead of calling an election because of the massive rebuke (which is often done), the Conservatives chose to install a new PM, Churchill. It was believed that Churchill would either fail and thus vindicate Chamberlain's policy stance, or Churchill would rumble along, without much success and thus allowing Chamberlain (still a member of the cabinet and Parliament) to run things in the background (which would have been easy to do as he was still very popular). Those outcomes however, would never come to fruition, and the rest they say is history!

Hope this answers some of your questions.