For the divider I'm not sure if 1k resistor and a 18uF capacitor will suit my needs...
I am not sure where you got these values from. An 18uF capacitor is very non standard, 10uF , 16uF and 22uF are the closest values.
However, it is not very critical as it is only a second order filter and the slope here is not steep.
You will have to experiment as to what PWM values you have to get to give those voltages to the fan. This is because you are relying on the non saturated part of the curve and it is not consistent from device to device.