Both the US and the UK gave up pretty quickly on the Walther Hydrogen Peroxide powered sub because of the continued explosions of the fuel. That was also a problem with the ME-163 Komet, as unused H2O2 had this nasty habit of exploding on landing, which was not very good for the continued good health of the pilot.
As for the myth that the ME-262 could have been in combat earlier, that is just what it is, a myth. The problem was engine unreliability, and the fact that not until the Germans had a look at the landing gear of a P-47 did they come up with the final gear for the ME-262. The test pilots hated the engine of the ME-262 as they never knew when it was going to fail, only that it would.
Not sure where you get the idea that the Germans were ahead in Nuclear Fisson. The ALSOS mission documents definitely do not show that, nor do they show any major interest in the idea. Nerve gas is a different story, and a bit more complex.
As for rockets, that depends. Liquid-fuel large rockets, yes. Although if Goddard had had the funding that Von Braun received, that might have been more than a bit different. Air to ground rockets for ground support, no. Nothing even close to the US 5" HVAR, or the 11.75" Tiny Tim. Air to air rockets, yes, because they had all of those B-17 to shoot at. Oddly enough, the Allies did not have that many German bombers to shoot at after 1941. Ground to air rockets would be a toss up between the UK and Germany. Ground to ground, about even, although the Germans never had anything close to the rocket barrages launched by the Russians, or the US during an amphibious assault.
Germany was way behind in aircraft engine development, mainly because of poor fuel and not having a good turbocharger for non-Diesel engines. As for the jet engine, which was developed by an Englishman named Whittle, if the UK had been able to devote a bit more time to research, rather than fighting a war, I suspect that they would have had a jet fighter a year or so earlier. The Meteor was used to shoot down V-1s. The Germans were a long way from anything comparable to the B-29, and the US had the B-36 under development. They never did have any carrier aircraft, although the British is some respects were in the same boat there. Transport planes were pretty much a US monopoly, with the German ones being hampered by having too many military characteristics build into them.