OK, so I just realised I left out a very critical piece of information, and I do apologise for this.
The "planned speed" field outputs an approximate maximum true airspeed at sea level. However, the performance figures that you see quoted for the real-world example aircraft on Wikipedia and elswehere are in true airspeed at their optimum altitude; at the high(ish) altitude that these aircraft will operate, the true airspeed will be much, much higher than the calibrated airspeed, which is what the aircraft "feels", for lack of a better way of putting it. Let me break it down a bit more for you:
Let's say we have an aircraft that can fly 220 knots at sea level, the calibrated airspeed and the true airspeed will be equal, under ideal atmospheric conditions. Now as the aircraft climbs to a higher altitude, it can still achieve that 220 knots of calibrated airspeed, assuming the engines can still produce the sea-level rated power. However, since both the air density and temperature have dropped as the aircraft climbs higher, the true airspeed starts to increase for a given calibrated airspeed. If this example aircraft is flying at 30,000 feet, and can still maintain 220 knots calibrated airspeed, its true airspeed will be 360 knots.
In future versions of the powerplant calculator (I might even make a revised version in the next day or so), I will include a tab with a chart that converts the planned speed to true airspeeds at different altitudes.
As a guideline, I wouldn't want to exceed a powerplant (as in, combined engine, gearbox and propeller) weight of 850 pounds each; more than that and you're starting to severely eat into your useful load. Obviously, less is better, so always strive for the least possible weight!
I should also mention that in the majority of these challenges going forward, it will no longer be possible to both fill the fuel tanks and fill all the seats with standard-weight passengers; this is a common condition in aviation and just something we have to live with on a daily basis, so don't fret if you find you can only fit five standard-weight passengers into this aircraft with full fuel. Beechcraft themselves quite bluntly say that their King Air 250 can only carry five passengers with full fuel.
Unfortunately for this challenge it is two engines only. As for noise, well, you can go into the red zone if you like, but you do it at the risk of losing points to your competitors.
As a suggestion, if you want to dramatically lower your noise production, consider adding more blades to the propeller and either a) turning it slower, or b) going to a smaller diameter. Real-world aircraft in this size category have up to five blades in their propellers, after all.
Yes. That figure tells you the total amount of power you need to go that fast.