From the 200/200C POH. Note these are not Raisbeck modified KingAirs!
When looking at the figures remember that you are dealing with an FAR23 certified aeroplane. In a nutshell all it is required to do is maintain a positive rate of climb on one engine up to a certain height.
Beechcraft offer the computations and charts for a balanced field length. They state that it is possible to reduce weight to "obtain the performance specifications of FAR 25 during the critical takeoff and initial climb segments. ...full compliance with other regulations applicable to FAR25 is not implied." It is quite an involved process and a lot of iterative calculations need to be performed.
(the example they use is on a hot day at 5000' field, 2+kms of rwy and 10 kts headwind, you need to limit your weight by 2000 lbs below MTOW!)
So the following answers deal specifically with non FAR 25 charts
Do the King Air have a published V1, VR and V2 for each weigh & temp?
They publish a rotate speed and a 50 foot speed for different weights (Vr is always 95kias and 50' is 121@12500 down to 108kias@9000lbs.
V1 equals Vr according to the notes.
In case of a engine failure at V1, will the King overfly the runway end at or above 35 ft? Refer the charts and the comments above. If light yes, it should.
What V1, VR, V2 and VREF is common to use?
See above figues. Approach Speed (they don't use the term Vref) is 103kias@12500lbs down to 93@9000.
Can you use reduced thrust (or assumed temperature) on takeoff?
Why would you want to make a performance that is marginal even more so?
Any problem in reducind prop rpm first, before reducing the torque, at the first reduction after takeoff?
Yes - your torque will go though the limits. Takeoff torque @ 2230ftlbs . RPM @ 2000. we reduce to 2000ftlbs and 1900 at first power reduction (LSALT at night/IMC). To easiest procedure is reduce the power to 1900ftlbs and then pull the props back to 1900rpm. The torque will rise to about 2000ftlbs then and only small change necessary to peg it exactly.
A lovely machine to fly. A tad thirsty perhaps, but a new Kingair climbs out like a homesick angel. As for the pressurisation - it's pretty simple really. Before t/off set the pressurisation controller to the cruise alt plus 1000 and before TOD set the airfield elevation plus 500' (there is a chart to be more specific if you must). Wind it slowly to begin with to avoid cabin drop, but it works fine. Smoother than the PC12's pressurisation controller!