It is a common misperception that the United States simply sat on the sidelines during the early part of World War II, ignoring the plight of the countries fighting the Axis powers, until the Japanese attack on Pearl Harbor in December 1941 finally roused the US. In actuality, the situation was much different. Once the war broke out in Europe, the US, although remaining neutral, consistently and increasingly committed its resources and forces to help countries threatened by the Axis. When the Axis threat grew as Germany conquered country after country, the US responded with increased assistance and aid to the beleaguered Allies.
In 1939-41, a neutral US changed its laws so that Allied nations could readily obtain US military equipment. Prior, US law required a mandatory arms embargo for all countries at war ("belligerents"), a mandatory ban on loans to belligerents, and a cash-and-carry requirement for any trade in non-embargoed goods with belligerents (the belligerents had to pay up front and had to transport the goods without using US merchant ships). These restrictions reflected the common belief in the US after World War I that the US had been tricked into the war by war profiteers and later taken advantage of by its allies who refused to repay their American war loans. (Britain, for example, owed $4.4 billion, which it never repaid.)
Days after the German occupation of Czechoslovakia in 1939, the US president, Franklin Delano Roosevelt, started trying to change the law so that the US could aid other countries. The proposed revisions died without passage in Congress in the summer of 1939.
Then the Germans invaded Poland in September 1939. Roosevelt again attempted to get the law revised, and this time Congress passed it. Although the provision banning loans to belligerents remained intact, the arms embargo portion was repealed, as long as trade in arms was "cash and carry." This change, however, was quite significant, and both Britain and France immediately took advantage of it, placing orders for military equipment and weapons at US firms, such as for hundreds of badly-needed combat aircraft. Significant deliveries of this equipment had begun in the spring of 1940, unfortunately about the time the German blitzkrieg knocked France out of the war.
As France tottered in June 1940, Roosevelt circumvented the Neutrality Act by declaring that many artillery pieces and millions of rounds of ammunition were "surplus" to US needs and thus could be disposed of as the president ordered—and he ordered them sent to Britain. In actual fact, of course, these were not surplus, as the US actually did not have sufficient military equipment for its own needs in case of war.
After the fall of France in June 1940, the US stepped up its efforts to aid countries fighting the Axis. By executive order, in September 1940, Roosevelt proclaimed the "Destroyers for Bases" deal with Britain. Britain and Canada acquired 50 older US destroyers (43 to the Royal Navy, 7 to the Royal Canadian Navy). In return, the US received 99-year leases for various naval and air bases on British possessions in the western hemisphere, including Newfoundland (then a British colony and not part of Canada), Bermuda, the Bahamas, and the Caribbean. The destroyers were ex-World War I ships that the US had recommisioned in 1939 and 1940 for US neutrality patrols. The British used them for many duties, especially convoy escort. Most famous of these destroyers perhaps is HMS Campbeltown (ex USS Buchanan), which was packed with explosives and blown up to destroy the St. Nazaire dry-dock during the famous Commando raid of 1942.
Roosevelt also allowed British pilots to train in the US and British ships to be repaired in US ports. Later, Roosevelt transferred US Coast Guard ships to Britain and allowed British Royal Navy ships to refuel and repair in US ports.
By late 1940, it became clear that Britain lacked the cash to purchase all the arms it wanted from the US, so the Lend-Lease bill was proposed. Congress passed it in March 1941, with billions of dollars allocated to it. The US also seized Axis ships present in US ports and used them for Lend-Lease shipments.
In 1941, the US sent forces to guard Greenland and Iceland. The US hemispheric security zone was extended eastward, so that Greenland and the Azore Islands were included in it. US Navy ships begin to attack German U-Boats they encountered.
US Navy aircrew went to Britain to help train British aircrew on using US-acquired naval aircraft. In May 1941, the Bismarck was spotted by a British PBY Catalina that was made in the US and was being flown by an American pilot. Also that month, Roosevelt declared an "unlimited national emergency" to ready US forces against attack by Axis belligerents and to increase US military production. Soon thereafter, the US seized foreign merchant ships in US ports to use for transporting goods overseas.
In June 1941, after the German invasion of its former semi-ally, the Soviet Union, the US released previously-frozen Soviet funds in the US.
In August 1941, the Atlantic Conference between Roosevelt and Churchill occurred. The public result was the Atlantic Charter, which eventually lead to the creation of the United Nations. Secret agreements covered the conduct of the war against the Axis by the US and Britain, including no separate peace deals, US defense of British possessions, opening a second front in Europe, and scientific cooperation over building an atomic bomb.
In September 1941, the undeclared naval war between the US and Germany ratcheted up, with the USN being issued "shoot on sight" orders.
In October 1941, the US extended Lend-Lease to the USSR and quickly committed to deliver over a 1,000 tanks and 2,000 aircraft in the first six months. The bulk of Lend-Lease, however, continued to go to Britain and the Commonwealth. By late October, Lend-Lease appropriations authorized by Congress reached 13 billion dollars (by some calculations, this is equivalent to 215 billion dollars in 2014).
Rather than sitting around in isolation in 1939-41, it is clear that the US consistently took substantive steps to aid countries fighting the Axis and in 1941 was neutral only in name but fully committed to helping Britain and the Commonwealth.
Iceland's status in WW2 is interesting. Denmark ruled Iceland from the 14th Century to 1918, whereupon it became a "free and sovereign" state under the Danish monarchy. Denmark continued to handle Iceland's foreign relations, even after WW2 started. Note that "free and sovereign" is not the same as "independent," and in April 1940, when Denmark was invaded and occupied by Germany, Iceland declared its temporary independence from Denmark and asserted its neutrality. In 1944, this temporary status became permanent when Iceland declared itself an independent republic.
So, in Europa terms, is Iceland an independent country in 1939? Good question. It was less of an independent country than the Dominions (Canada, Australia, etc.) of the British Commonwealth, which had the British monarch as their own monarch. It was much more independent than most possessions of the British Empire (these were under the British monarch but were not necessarily part of the UK itself). Overall, the best indicator is that the Icelandic home government felt it necessary to declare independence (temporary at that) in 1940, so Iceland should start as an autonomous part of Denmark but can subsequently become independent.
Iceland has another ambiguous status in WW2: In May 1940, British forces landed in Iceland against the wishes of the Icelandic government. Following the German occupation of Denmark, Britain offered to protect Iceland. Iceland declined the offer. The landing and occupation meet no armed resistance, but Iceland issued a formal protest against the action. Certainly Churchill's view that "Small nations must not tie our hands when we are fighting for their rights and freedom," which he first stated in regard to Norway in 1939, also applied to Iceland.
So, did Britain invade Iceland? While you can argue it either way, perhaps the most telling point is what the Icelandic government actually did after issuing its protest: nothing. The occupation not only was not contested, but the Icelandic prime minister called Britain a friendly nation and requested that Iceland's inhabitants treat the occupation forces as guests. Later, in 1941, when the still-neutral USA offered to take over protection of Iceland (so that British forces there could be used elsewhere), the US required a request for protection from the Icelandic government before sending any forces. The Icelandic government, which indeed had in July 1940 discussed with the US being placed under US protection under the Monroe Doctrine, issued a cautiously worded request for protection.
Q: Did WW2 Iceland have any kind of local defense forces at all?
A: Iceland supposedly never has had any military forces in the modern sense (it certainly had heavily armed warriors running around when it was first settled). It did have a small coast guard, but probably nothing that'd show up at Europa level forces. On land, I believe the police handled internal security, but they were by no means militarized.
Q: Did Denmark in the 1930s ever station any forces in Iceland?
A: Off hand, I'm not sure, but I suspect no ground forces were stationed there. Denmark was responsible for Iceland's defense, but probably no forces were needed or wanted.
Q: What if Denmark actively resisted the German invasion and its government went into exile. How would Iceland be affected?
A: It's hard to tell. Icelanders from the little I know tended NOT to regard Denmark as the "mother country" the way many citizens of the Dominions regard Britain. (Indeed, Iceland originally was independent, then became part of Norway, then became part of Denmark after Norway and Denmark became a united kingdom, and then stayed under the Danish monarchy when Denmark had to cede Norway to Sweden near the end of the Napoleonic Wars.) I suspect Iceland would have sought to remain neutral.
During the Great Patriotic War (the Soviet's name for their part of World War II), the Red Army used the term "corps" for two very different types of military ground-force organizations: "command" corps and "combat" corps. (Command and combat are terms I use to distinguish the two and were not official Soviet terminology.)
At the start of the war in June 1941, the Red Army had numerous command corps, which were headquarters to control ground forces like in most other armies in WW2. For example, rifle corps controlled several rifle divisions (plus other units), similar to German infantry corps; mechanized corps controlled two tank and one mechanized divisions (plus other units), somewhat similar to German panzer corps; and cavalry corps controlled cavalry divisions (plus other units).
The impact of the German invasion quickly showed the inefficiencies and ineptness of the Red Army. One problem that emerged was, due to Stalin's purges, many Red Army officers lacked the experience or competence to handle large formations. Most of the mechanized corps were smashed in battle and disbanded during the summer of 1941. At the same time, the Soviet abolished rifle corps in their command structure: army headquarters directly controlled the rifle divisions (plus other units). While this theoretically reduced the flexibility of army HQs, in practice it allowed the Soviets to have their most competent senior officers handle large formations effectively without having to filter their orders through less-competent corps HQs. Not all command corps were abolished (cavalry corps, for example, were used extensively), and the Soviets gradually brought back rifle corps in 1942 as the abilities and experience of their officers increased.
Combat corps appeared in 1942. A combat corps was not a command headquarters to which various units could be attached as the situation demanded. Instead, it was an exact equivalent of a division, with a fixed, standardized organization of sub-units. For example, a tank corps would have three tank brigades, one motorized rifle brigade, and various smaller sub-units, similar to how a rifle division would have three rifle regiments, an artillery regiment, and various smaller sub-units.
So, if a combat corps was equivalent to a division, why did the Soviets use different terminology? I believe (I do not have a definitive reference on this) that the distinction between combat "corps" and "divisions" in the WW2 USSR was due to a very traditional approach to nomenclature: A combat division was composed of regiments. A division could not be composed of brigades. However, by 1942, the basic tank unit was a tank brigade. Not only were the mechanized corps smashed and disbanded in 1941, almost all the tank divisions suffered the same fate. (In the main theater of war, the few that survived to December 1941 typically were greatly understrength and either were redesignated brigades or were disbanded.) Instead of tank divisions, which were intended for large-scale mechanized operations that the Soviets couldn't handle at the time, the Soviets needed tank forces better suited to provide armored support for the rifle forces. The tank brigade was well-suited for this, and the Soviets accordingly raised numerous tank brigades.
In 1942, a number of these tank brigades were grouped into division-sized formations, to start rebuilding the Red Army's ability to conduct mechanized operations. However, since a division could not control brigades but a corps could, these new formations were called tank corps. Later in 1942, an improved tank corps, called the mechanized corps, also containing brigades, was organized.
If you are familiar with Soviet wartime organization, you may be aware that the late-war Soviet artillery divisions were composed of several artillery brigades. Doesn't this violate the divisions-must-have-regiments theory? Not really! The artillery divisions were first organized in 1942 and contained artillery regiments. It was only later in the war that the Soviets reorganized their artillery into brigades.
Finally, I note that soon after the war ended, the Soviets redesignated their mechanized and tank corps as divisions, with the former component brigades being reorganized as regiments. So, I believe the wartime combat corps was a terminology expediency the Soviets adopted due to circumstances and abandoned as soon as practical.