Dear Mustafa,
How long the solution will take to converge to steady state depends on the turbine you modeling, the degrees of freedom enabled, the initial conditions you’ve set, and the wind conditions you are operating with. I can’t really comment in general.
The rotor inertia is not documented in the NREL 5-MW baseline turbine specifications report, but it can be calculated by running the FAST model (the rotor inertia is written to the FAST summary (*.fsm) file).
Regarding the gain scheduling, all you really need is the slope of the curve of ∂P/∂θ versus θ. Selecting θk as the value of the pitch that gives ∂P/∂θ = 2*∂P/∂θ(θ=0) is just a convenient way of calculating the slope. But I don’t really know anything about your turbine, so, can’t really comment on whether the values you are reporting make sense.
Best regards,