For a commercial operation, the aircraft dispatcher. For a private pilot flying on their own, the pilot is responsible. Charter operations vary, its the pilots responsibility but some choose to hire flight planners and/or dispatchers as well and the responsibility is delegated to them.

The numbers and charts are found in the airplane manual for small aircraft, for commercial jets a separate manual is generally produced for the performance charts; my airline calls it the Operations Data Manual, or ODM. Our engineering team has gone through the ODM and coded all of the numbers into our flight planning system, so that as we plan the flight and update items like passenger count and the weights for checked bags and cargo, the system automatically updates and displays the numbers for those conditions for us to cross check and verify.

As a pilot and someone who plans these numbers for dozens of flights on passenger jets everyday at work, I can confirm that the Vr is not static. It changes based on weight, flap/slat configuration, headwind/tailwind, temperature, ambient pressure, location of the CG… all of it affects the V speeds and they do very much change.

Depends on the jet and how much payload and fuel it’s carrying. Also depends on the airport, altitude, temperature, obstacle clearance requirements, etc. I have planned and dispatched 777’s off 13000’ runways where we were bumping cargo to other flights due to poor takeoff performance.

Runway length is only 1 piece of a very complicated formula for determining payload allowed, its called Runway Allowable Takeoff Weight, or RATOW - this number can be higher than structural, in which case structural would be the weight limit, or it can be much lower depending on a whole host of factors, in addition to the length of the runway and the amount of headwind or tailwind.

Incorrect. Headwinds improve performance, short distance required, and lower the Vr (speed at which rotation is initiated). Tailwinds, even for big jets, have HUGE performance penalties.