In terms of speed: please find a photo of Walter J Boyne's book "The Best of Wings". He quotes program test Gerd Lindner pilot as saying it could achieve 565mph at 16,400ft (that would have been 925kmh at 5000m). He was a professional test pilot, not a factory acceptance pilot or a fighter pilot. He's paid to be technically accurate. Smooth surface, maybe filled in, well aligned airframe, well aligned engines, good pair of engines.
Lindner also notes he nursed a pair of engines to 60 hours on the wing. The official Jumo MTBO was 25 hours and on the basis of spare parts production the Germans expected 4 x 25 hours life out of the engines. The Luftwaffe maintenance crews, the blackbirds were possibly pulling them early. It is also important to note that the hollow air-cooled blades of the Jumo 004B4 only reached the front in November 1944 or so and so air cooled blades were likely quite rare.
Vampire Performance Trials
Meteor Performance Trials
P-80 Performance Tests
Note these are mostly post war tests. Meteor had 4 engines Welland (two ratings), Derwent I, Derwent II (two ratings) and finally Derwent V which was a scaled down Nene that only saw service in 1948 on the Meteor F4 though it was flight testing in 1945 and broke some sea level speed records (where Mach wasn't an issue)
Note the Faster P-80's of 1947 fame received clipped wings and modified nosese to increase speed. P-80B added ejection, P-80C much improved.
The fuel control system of the Jumo 004B was as follows
1 Gear driven pump set to supply slightly more fuel than would be needed at sea level full thrust.
2 Pressure relief regulating valve converts this to a constant pressure.
3 Pilots throttle open a valve whose degree of opening determines fuel flow rate: this spools up the compressor.
4 Between the pressure valve and the throttle was also a centrifugal governor, also set by the pilots throttle, that regulated the engine RPM.
An exhaust cone acted as a variable area nozzle in response to engine back pressure, it should have helped regulate air fuel ratio a little but didn't help much.
April should have seen the deployment of the 'beschleunigungs ventil' or 'accelerator control valve' that measured the air flow rate and adjusted the fuel in proportion to it so that rapid throttle movement by the pilot wouldn't flame out or burnout the engine when it was accelerating. Come back in a few days and I will post a link to proof of this device.
The Jumo 004B couldn't get much above 38000ft because the compressor could surge, the cure was reducing RPM below the critical speed of 8700 rpm which of course would reduce thrust. At low fuel flow rates during low thrust or idle or at above 38000ft the fuel flow rate was so low the nozzles could not provide the correct vaporisation which could flame out the engines. The 'cure' was to be duplex nozzles from the L'Orange company (Oscar L'Orange was a colleague of Robert Bosch). Duplex nozzles switch to a second set of nozzles at low flow rates set to provide a better spray/vaporisation pattern.
There was a new unrestricted RPM compressor under development which might have seen instalment in the Jumo 004D at the end of the war, Nowara says these engines, without RPM restriction, were starting production but not seem to have been found but were supposedly rated at up to 1100kP (instead of just 880kP) There was also a Jumo 004C good for about 950-1000kP.
These engines are somewhat of a mystery though.
Either way the accelerator valve and duplex nozzles would have added greatly to Jumo 004 handling and reliability even though compressor RPM couldn't be raised.
Arado 234C3 is quoted as capable of 560mph specifically with BMW 003A1 engines in David Myhra's book "Arado 234C" its a rather large 450 page tome with pictures of David visiting with Rudiger Kosin the designer. It's possible this is the estimated speed with the BMW 003C but I doubt it as Myhra is at pains to list details on a doxen different variants,. There was a lot of thrust here 4 x 800kg = 3200kg/7240lbs. By far the most powerful WW2 jet by far.
The bombs were carried semi recessed beneath the fuselage and engines. A bomb as big as 2000kg could be lifted. Given the high speed and high power it wasn't going to slow too much. William Green's book quotes 515mph with a Hs 293 or 294 glide bomb, a rather ungainly winged and rocket boosted device.
The BMW 003C was never built but the compressors had been built and benched, the hot section was the same. The BMW 003E of He 162 was the same as BMW 003A apart from the accessories gearbox and had a 900kg overload thrust emergency rating for 30 seconds. Probably most useful in take-off and a quick acceleration to operating speed.
I doubt any WW2 allied jet exceeded 500mph during WW2, the meteor was at either 466mph or 482 at the end of WW2, it reached 495 and finally 515 at the end of 1945.
The speeds are well covered in ww2 performance testing: I'll link to it at the end of my image.
Tempest V stalled without warning or buffet and flipped to opposite bank. Unpleasant.
P-51H was considered suitable for carrier use, due to the longer tail. The wings on the P-51 were always good.