Bear in mind, 390 mph is the true airspeed: what a radar gun would measure from a balloon floating at 20,000 feet when the P-39 is flying directly toward or away from the radar. But due to the reduced air density at altitude, if you put your hand in the 390 mph airstream it would feel like a sea level speed of "only" 290 mph.
That latter speed is what the P-39 airspeed indicator would show. (I omit the correction for "installation error" since I don't have the data at hand.) It's possible to build a totally mechanical indicator for true airspeed (some postwar aircraft had them, usually at the navigator station), but they're much more complex and actually less useful to the pilot. To avoid structural failure due to overspeed or stall due to underspeed, it's easiest if you have an indication of the force of air hitting the airplane, in terms of the equivalent sea level speed. Then the redline and stall speeds are the same regardless of altitude. For example, when landing at a high altitude airport it's not necessary to adjust your final approach speed upward to compensate for the thinner air. Just fly the same indicated airspeed that you use at sea level and you'll be safe.
For airplanes with the performance to reach critical Mach, the redline indicated airspeed does depend on altitude. For instance, P-38 red line is 420 mph at 10,000 feet but only 290 mph at 30,000. The pilot manual says you can safely go 20 mph faster if the airplane is equipped with dive recovery flaps, but no more.
The Vought F4U Corsair became the first single-engine fighter to exceed 400 mph when it went 405 mph on 1 Oct 40 between Stratford to Hartford, Connecticutt, U.S.A. . Production units were not that fast until later in the F4U's life.
No, it wasn't. We've already had that discussion further up the thread. The eighth prototype He 100 set a world speed record by reaching 463mph (746 km/h) a full year before the F4U. As for the seaplane racers, *rolls eyes* yes, we know they are not fighters, they were mentioned by me as the first aircraft to exceed 400 mph, out of interest.