The problem with the Germans was that while they sank money and resources into advanced projects like rockets and jets and missiles and cool stuff that everyone believes meant they were more advanced than everyone else, we forget that the Germans didn't get some of the basics right. Had they concentrated on these, perhaps they might have been able to have lasted longer - of course it is to our benefit that they didn't.
No objection there. Nazism needed to be utterly crushed, and it was good that it was. Not that Soviet communism was much better, but alas..
They never got a 2,000 hp plus engine into production and service, their advanced four engined heavy bomber programme Bomber A was a failure, resulting in one of the worst aircraft of the war, the He 177, their replacement fast bomber programme Bomber B was also a failure because they couldn't get their 2,000 hp plus engine to work, which meant that aircraft of pre-war vintage were kept on in service for far longer than they should have been. The He 111 was still in the Luftwaffe's frontline in 1945, equating to the RAF relying on the AW Whitley, or the USAAF relying on the B-18 Bolo in that time.
The Me 262 and He 162 were highlights, but were troubled because of their unreliable engines and the reliance on forced labour for their manufacture.
Yes, and no. I'm not sure a 2000 hp engine, per se, would have been that necessary. The Allied heavy bomber fleets that flattened Europe were using ~1200 hp engines, and the arguably best piston fighter of the war, the Mustang, didn't have a 2000 hp engine either. The Allied 2000 hp engine equipped planes certainly helped, but honestly I don't think the air war would have been lost without them either. But the goal of powerful next generation piston engines is perhaps instructive of the German engine development effort flailing in all kinds of directions instead of focusing on improving their basic engines (605/603/213), which still had plenty of potential left in them.
As for the jets, yes it was very early days for jet propulsion and they suffered from all kinds of problems. However, I'd also argue that jets represented one of the few ways that could have allowed the LW to face the onslaught of Allied air power from say late 1943 onwards. Incrementally better piston engine aircraft weren't going to cut it anymore.
The cost of the way in which the Third Reich was run was directly responsible for Germany's failures. The fostering of internal squabbling, currying favour, self-promotion and outright sabotage of competitors' plans was no way to run things during a war footing, but that's how they did it.
This is, generally, how dictatorships work. The strongman at the top stays at the top by playing the various factions against each other and have them compete in bootlicking. It's inherent in how the entire system works. Nazism, fascism, communism, it's all the same.
Democracies may seem weak and impotent, endlessly debating things in public. But once they decide to act, they are immensely powerful.
There might be a lesson here for the modern world as well..