As you suggest~~, and /u/GodoftheCopyBooks aptly puts it,~~ military defeat was a largely taboo subject in the mass media of the era (as a film historian I should add that this included your weekly or biweekly newsreel in addition to newspaper and radio!) – and following the crackdowns around 1931, there wasn't any sort of politically-alternative press to speak of. So in a strictly factual sense, the public didn't "know" that the war was being lost.

That said, there's a general consensus among historians that the Japanese people were nevertheless mostly aware that they were losing the war. Their lived experience of deprivation, suffering, and death was simply too out of synch with the official line to permit any other conclusion. To take a few statistics out of John Dower's book Embracing Defeat,

3-4 percent of the 1941 population had died, plus millions more injured and/or malnourished

one-quarter to one-third of the country's wealth destroyed

66 major cities heavily bombed, inc. Tokyo where 65% of residences were destroyed

9 million homeless

...etc. Material scarcity, hunger, the death of loved ones, and the daily struggle to survive were what were on people's minds from at least 1943 on; by the end of the war, most people simply didn't care about winning the war anymore, and the announcement of defeat was greeted in many quarters with a sigh of relief.

As to your last question, all of these phenomena were easily incorporated into ideological templates that had been in place since at least the late 1930s. Bombing raids on the homeland? The US were a monstrous foe who put so little stock in human life that a photo of the severed head of a Japanese solider mounted on a tank could be featured without condemnation in Life Magazine. Deceased rations? Austerity was the only ethical condition for a country whose men were off fighting a war; "Luxury is the Enemy!" as the famous wartime slogan went. Recruiting, likewise, simply represented the depth of the people's commitment to their emperor whose national body preceded and subsumed them.

If you wanna see what celebrations of the Pearl Harbor victory looked like, take a peek at War at Sea from Hawai'i to Malay (Yamamoto 1942), a reenactment released on the one-year anniversary of the attack.

Edits for clarity.

2nd Edit: Curious myself, I looked up the March 11, 1945 Tokyo Asahi Shinbun, one of the major Tokyo papers on the day after "Operation Meetinghouse." The morning edition headline reads, "Approximately 130 B-29s Indiscriminately Bomb Tokyo City."

3rd Edit: If you're looking for more information, I highly recommend:

• John Dower, War Without Mercy: Race and Power in the Pacific War

• Peter High, The Imperial Screen: Japanese Film Culture in the Fifteen Years' War

• Ben-Ami Shillony, Politics and Culture in Wartime Japan

(Actually I haven't read this last book, but there's a whole section about the wartime press, p. 91-97, that gives more information about the timelines involved; e.g. "In 1937 all items concerning national economy and foreign relations were designated as state secrets that could not be published without the prior consent of the authorities" (93))

Hopefully someone with more knowledge comes along, but for now here is something.

Though the public didn't know it, a few Japanese admirals(Yamamoto) knew they lost the war when they failed to destroy America's aircraft carriers at Pearl Harbour and again at Midway.

By 1945 the public knew they were losing it. The Americans were bombing Japan's largest cities, destroying their industrial base. They had lost Okinawa, the edge of the home islands. The Americans had retaken the Phillipines and controlled the seas surrounding Japan. Though these details may not have been known exactly, their effects were being felt by the Japanese public.

American bombings practicality destroyed nearly all Japan's cities except for the potential targets of the atomic bomb (Kyoto, Hiroshima, Kokura, Niigata and Nagasaki in that order). The firebombing of Tokyo was particularly brutal. Thousands were dying in their homes, there were a million internal refugees, food was short and industry was constantly being shuffled around as bombing runs were constantly destroying it. It is not hard to imagine that the public knew they were not exactly winning. It is hard to imagine the political culture in Japan at the time though. It was believed the Japanese were racially superior, guided by their divine emperor. That though they were losing all these resources, it didn't matter because the Japanese were pure blooded and had a strong fighting spirit. As they planned operation Ketsu-Go (their last defense on the island of Kyoshu), they had many more kamikaze volunteers than planes to give them. As the Americans fought to take Okinawa, both soldiers and civilians suicided en masse ("Suicide" and "Banzai" cliffs). They believed that through sheer will and racial superiority, that the war may not be won but salvaged as the Americans would grow tired quickly.

Of course, not all Japanese were so racist/stubborn/naive, and the leadership worried of revolts late in the war. But enough were that it took the atomic bomb and Soviet betrayal for "peace-feelers" to finally end the war.

References:

My knowledge comes from what I know about the decision to drop the atomic bomb, but I think some aspects are relevant to your question.

ULTRA military intercepts

MAGIC diplomatic intercepts

Racing the Enemy by Hasegawa

The Columbia Guide to Hiroshima and the Bomb by Kort

Downfall by Frank

The Most Controversial Decision by Miscamble