Were the Japanese pilots aware of the inferiority of their aircraft designs?
How were tactics changed or adapted as the war turned against their favor?
Were any Japanese fighter plane designs (Besides the Ki-84) on equal terms with American equivalents?
Are there recollections available of Japanese pilots who may have survived the Marianas Turkey Shoot?
Was morale privately affected by witnessing many friends shot down or sent on suicide missions?
Were there any Japanese flyers who downed late war American fighter planes (F6F, F4U, P51, P47) on multiple occasions?
This is an interesting and diverse set of questions. Some are very simple to answer, some not so much.
Let's start with the simple ones:
5.) Of course. All these men were humans after all and the emotional impact of losing your friends, your battle brothers, is undeniable.
6.) Of course. Well, probably not the P-47, as those were somewhat rare in the Pacific theater. The scale of the combat was just too expansive for there to be barely any losses of 'late war' US aircraft. So of course, F6Fs, F4Us, P51s were still shot down with some amount of regularity within the scope of the entire Pacific theater.
1.) is an interesting question. The answer is of course yes, but it merits some deeper explaining. First off, you can't really fool a fighter pilot. They will know real fast how the cards are, especially regarding their own aircraft. The Japanese pilots were definitely aware how their aircraft stacked up against the opposition, whether positive or negative. The famous A6M Zero was practically unrivalled when it was introduced. Fast (back then it was!), good climber, strong cannon armament, excellent range and ridiculously agile for a monoplane design. In its early days, the Zero could outfly most things the US could throw at them and the Japanese knew it. But of course, when the tides turned, the Japanese pilots realized the shortcomings as well. When speaking about the Zero specifically, Saburo Sakai or Minoru Honda said it was a plane for aerobatics, not war. The light construction and propensity to catch fire were universally seen as severe drawbacks by the Japanese pilots. They loved the agility, but they knew their aircraft could barely take a hit. This contrasted in the extreme with the rugged Grumman F4F Wildcats of the USN and it was a trend that was to continue with the equally rugged successor the F6F. The F4U, P51, P38 and other aircraft the US used may not have possessed the near-mythical durability of Wildcats, Hellcats and Thunderbolts, but they were still absolute tanks compared to the rather flimsy Zero. And despite having a fair amount of fighter types and designs, the Zero, in all its updated guises, remained the dominant IJN and IJA fighter (<= slight mistake, see Mene's post below). In addition to being flimsy, the Zero's design lent itself poorly for higher speeds, which became pre-dominant in fighter combat during WW2. With such a speed difference to overcome, the Zeros were quite vulnerable. And again, of course the Japanese pilots knew this. Just as they knew their superiority over the Wildcats in the early days, they realized their technical inferiority now all the more.
Another interesting feature that you find when you look at Japanese evaluations of captured American aircraft; Japanese pilots generally express appreciation and not a little amazement at the quality of the on-board equipment of the American aircraft. The radios especially were highly praised, as were spacious cockpits, heater-cooler systems and pilot comfort considerations.
Having said all that, regarding question 1 and 3, there of course always remains the fact that 'which plane is better' often hinges on, partially at least, the subjective opinions of the men that flew in and against these aircraft. So one Japanese pilot's opinion on the Zero or the Hayate might very well differ from the next's.
Regardless, I think it's perhaps best to hear some things straight from the horses' mouths. Here are two Japanese interviews with Saburo Sakai and Minoru Honda, uploaded and translated (subtitled) by a very nice person in the War Thunder community. I'm not quite sure when these interviews were done, I'm guessing the 90s somewhere, maybe early 2000s (Sakai's was in '75 I see now). The men are old, obviously, but still sharp. The interviewer asks good questions and our WT friend did a great job on the translations.
I definitely suggest you watch these two interviews; they won't answer all your questions straight up, but it's definitely relevant to the topic and undoubtedly interesting for you if you are fascinated by WW2 aerial combat.
https://www.youtube.com/watch?v=JitLr5D7LSI Honda Minoru part 1
https://www.youtube.com/watch?v=3H_9iR7zvMk Honda Minoru part 2
https://www.youtube.com/watch?v=9H4Ed7_F-rs Honda Minoru part 3
https://www.youtube.com/watch?v=824I_anxW-w Saburo Sakai part 1
https://www.youtube.com/watch?v=F7mKM4mEGNk Saburo Sakai part 2
The Minoru Honda interview especially is so recommendable. The old ace is still sharp as a knife, doesn't talk a lick of gibberish whilst being very candid about his experiences and opinions. I know of course the sub's rules regarding personal accounts, but I'm fairly certain that an in-depth interview like this is very relevant to the topic of this thread.
edit: rewatching the interviews cos ive only seen em once since leon uploaded them, but when Minoru says about the Zero's utter lack of armour: "No one goes to war in a bathing suit!", it didn't fail to crack me up just like the first time.
Oh and ofc, as far as sources go: well, hmmm, mostly accumulated knowledge over the years. Regarding literature, pilot accounts are always indispensable when it comes to understand aerial warfare. That doesn't mean take everything they say for historical gospel, especially when it comes to bigger picture matters. But the accounts of the men that flew and fought in these machines can not go amiss in a serious attempt to understand more of the matter.
Regarding other good overview books of the Pacific air war, there are quite a few! Fire in the Sky by Eric Bergerud (??) is a pretty good one for starters.
Regarding technical details about airplanes, the internet is your friend, but it's very difficult to apply critical source selection and proper interpretation of sometimes vague-ish, not to mention feckin Japanese, data sheets. A lot of it is out there, though.
Certainly pilots who flew the Ki-43 did not regard it as especially inferior even quite late in the war. The feeling was that since it could out-maneuver almost anything in the sky, so long as a pilot could avoid being surprised then he had a good chance. Of course, the JAAF was always wedded to the idea of maneuverability as the prime characteristic in a fighter, but the Ki-43 was amazingly giving a good account of itself even in 1944 in the hands of pilots such as Saburo Nakamura, Goichi Sumino, and Hideo Miyabe. All used the aircraft to down such adversaries as Spifire VIIIs and Mustangs. Retrospective analysis shows that Ki-43s were never being destroyed in huge numbers, they never suffered the attrition the Luftwaffe did late in the war. The JAAF was more whittled down by incremental losses and the inability to operate, for instance through lack of fuel and parts. However, this does not apply to the Philippines where losses were massive, though again largely on the ground.
A problem the Japanese had was a lack of organisational and industrial effort compared with the US and other Allies, so when the Sentai sent to the Philippines and New Guinea were decimated it was probably seen as a matter of being outnumbered rather than simply being out-fought.
But for the Japanese, this was in keeping with the samurai traditions that underpinned their military philosophies. They were less demoralised by being outnumbered, the Japanese miltary controlled education so His Majesty's warriors arrived at the front after being mentally conditioned for twenty years, with all that implies for the capacity for independent thought. The Japanese were also especially prone to over-claiming, especially as less experienced pilots came on board. A third factor is that Allied claims could be grossly over-stated: operations against Rabaul by P-38s and Corsairs resulted in massive claims, which are not borne out by Japanese loss returns (see Bruce Gamble: Target Rabaul).
As to aircraft quality, the Ki-84 nevre really came anywhere near its potential in part because by late war Japanese fuel was low octane and aircraft, especially high-performance aircraft, did not reach design performance (until the Allies captured and tested them with quality fuel and achieved results the Japanese pilots never could). The Ki-61 was always treated with respect by the Allies and was a very high performance aircraft in its very late Ki-100, radial-engined form.
When one examines Japanese aircraft, their inability to develop good engines in the 2000hp class was a key factor, one that prevented the early-war aircraft being replaced. Their industrial technology, which could and did make good 1000hp-class engines, was simply obsolete when it came to high compression ratios, turbochargers and so on.
It also really did not help that the Nakajima Sakae for the 5 years it was in service did not see a marked improvement in performance. The IJN were most likely very aware of the "inferiority" of their designs, but it wasn't for the lack of effort as much as the IJN like the rest of the Japanese military was terribly short of resources. Note that there were plenty of designs that the US approached with a reasonable amount of trepidation. Such as the Ki-61 and the rather well flying though terribly unreliable N1K series.
For the Americans, the development of tactics like the Thach Weave meant that untrained Japanese pilots would either have to dive to safety or get shot down due to superior coverage abilities.
Equivalent terms is a difficult way to evaluate as much of the performance of aircraft in WWII tends to be seen through the lens of either (and sometimes both) lethal ability and logistical need. Indeed on paper there were rather good designs such as the Ki-84 or the N1K-J which yourself and others have pointed out. Likewise the Ki-61 was no slouch as well. The problem however was that the designs were either too late or required an extra component of logistics that rendered deployment of them at best ineffective. To make matters worse the rivalry between the IJA and IJN catalyzed the lack of new designs as competing designs in a wartime industry strained by resource shortages meant that development for the aging Sakae to the new but unreliable Homare engines dragged on far too long.
Very likely, though due to my inability to read or speak Japanese I have not encountered many. I should look into that actually.
Most definitely. Near the end of the war many pilots were terribly unprepared and it did not help that internal conflicts within the IJA and IJN still persisted well into 1945. Suicide missions or not, the morale hit was very noticeable as the tide was being swiftly and surely turned in favor of the Allies.
I wouldn't consider any of those planes necessarily late war, but there definitely were pilots who shot down F6Fs, F4Us, and the like. In fact in a few notable cases, the early introduction of the F4U (which did not have a very favorable early combat record) actually had pilots who survived getting shot down. I believe the total tally from the Pacific was about 4,600 or so airplanes shot down in the Pacific Theater and a good portion of these involved either fighter planes or B-29s which were shot down on bombing missions on Japan.
Sources (the ones I have readily available, I may update later):
Williams, A.G., and Gustin, E. 2003. Flying Guns: The Development of Aircraft Guns, Ammunition, and Installations 1933-45. ISBN 978-1-84037-227-4.
Japanese Aircraft of the Pacific War, Rene J. Francillion ISBN: 978-0870213137.