I can't speak for German citizens, but Japanese citizens were quite aware that the war was not going well. Following the disastrous defeats at Midway and Guadalcanal, the war was clearly lost for Japan. In the US bombing raids, 67 Japanese cities suffered great damage resulting in several hundred thousand Japanese deaths and making about 5 million Japanese homeless. Most Japanese citizens at this point understood they were losing and trusted that their leaders would give up at a reasonable point. This sentiment is echoed in many Japanese oral histories. What is perhaps unique about Japan is the degree in which citizens embraced the idea of sacrifice to the nation. Housewives drilled with bamboo spears to prepare to attack any invading American forces, students were drafted to manufacture balloon bombs, which would travel in the prevailing winds to the Continental US. Another idea that is echoed in the oral histories of these individuals is that normal citizens felt obligated to sacrifice for the nation, as the front line soldiers had it worse. The Japanese Press was instrumental in instilling these attitudes in the Japanese people, but the Japanese were generally eager to assist the nation in whatever small, desperate way they could. To me, Kamikaze pilots exemplified the Japanese trait of sacrificing for the nation more than any. In interviews years later, pilots who were never sent on their suicidal attack flights noted that they were terrified of dying, but they were willing to if it meant saving Japan.

The Emperor and other leaders in Japan hoped for a more advantageous peace with the US which would guarantee protections for the emperor and prevent an occupation, hopefully with the Soviet Union acting as a mediator. After the atomic bombs dropped and the Soviet Union entered the war, this was no longer possible and Japan was forced to accept allied terms of unconditional surrender.

Sources: A wonderful documentary on the Kamikaze Pilots: Wings of Defeat

Bix. Hirohito and the Making of Modern Japan

Dower. Embracing Defeat

Cook and Cook. Japan at War an Oral History

Edited for formatting

The Nazi propaganda machine kept running until the very end of the war in Germany. After the defeat at Stalingrad in '43 more and more Germans started listening to foreign radio to get news. Movie theaters used to show propaganda films before the movie, but people started to reject them. Goebbels ordered the doors of theaters be shut before the propaganda film was shown. So if you wanted to see the movie, you had to watch the propaganda.

Near the end of the war the tone of the propaganda changed, focusing on what would happen if Germany lost the war. They used a leaked post-war plan from the allies that showed they wanted to destroy Germany's industry and turn it into an agrarian society. The aim was to re-invigorate the German population and urge them to resist the allies. Since the Nazi propaganda machine, in an indirect way, admitted things were going sour, the German population would have been quite aware of that fact.

Conversely, how aware were British, US, and Russian citizens of the fact they were winning?

At Archive.org, you can download and listen to American radio broadcasts of D-day. The first reports of the invasion came from German state run radio, and were not confirmed by the Allies until a couple of hours later.

(Source is Richard Overys 'The third Reich, a chronicle' page 291) an SD report was made after the loss of Stalingrad that relates to the reaction after such a cataclysmic defeat. Parts of it are relevant, the more relevant parts are in bold. regrettably, I do not know too much about the subject so can't answer too many questions but this should show you what the authorities knew about how aware their citizens where about the war turning against them

'The reporting of the end of the struggle in Stalingrad has once again had a deep impact on the whole people. The speech of 30 January and the Fuhrer proclamation are pushed into the background because of this even and play in the earnest discussions among the citizens a lesser role than a range of questions which are linked to the happenings in Stalingrad. In the first place the population asks about the scale of the blood sacrifice. The estimates range between figures of 60,000 and 300,000 men. As a result, people reckon that the greater part of the fighters of Stalingrad is dead. In relation to the troops fallen into Russian captivity people swing between two perceptions. Some declare that captivity is worse than death because the Bolsheviks will handle inhumanely the soldiers that have fallen into their hands. Others on the other hand insist that it is fortunate not everyone had fallen, so there is still some hope that the later part of them might return home. The dependents of the fighters in Stalingrad particularly suffer very much from this division of opinion and the consequent uncertainty. Further in all elements of the population the unavailability of the development in Stalingrad and the necessity for the monstrous sacrifice is discussed. In detail, the citizens are moved to ask if the threat to Stalingrad was itself not properly recognized. The air reconnaissance must have confirmed the approach of Russian armies sent against Stalingrad. The question is also asked , for what reasons the city was evacuated whilst there was still time. Above all it is observed that the strength of the enemy must have been underestimated, otherwise the risk would not have been undertaken, of holding Stalingrad after the encirclement. The population cannot grasp that the abandonment of Stalingrad and in part do not have a proper understanding of the strategic significance of the struggles, because of a lack of precise orientation about the whole development of the southern sector of the Eastern front. In part it is doubted that the defenders of Stalingrad in the end tied down strong forces of the enemy. The third point around which the discussions of the citizens revolve is the significance of the struggle for Stalingrad in the whole course of the war. There is a general conviction that Stalingrad signifies a turning point in the war. While those of a fighting nature feel Stalingrad as an obligation for the final mobilisation of all forces at the front and at home, from which mobilization they hope for victory, the more feeble citizens are inclined to see the beginning of the end.'

It's not exactly original source material, but "The Tin Drum" has some excellent scenes related to this. In the beginning the father eagerly listens to the radio and plots the victories on his maps; later the radio plays and the father doesn't bother to map the retreating "victories".

Did any kamikaze pilots take off, then turn around and hit their own ships/bases/cities with their suicide planes?