It appears you are on the correct track, the drawing is great. Here is a tool that will help a you a lot: Ohms Law Calculator It is an online calculator. You can use this to check your wire sizing. I cannot check that because I do not know how much the motors pull but you can using the calculator. Another link: Voltage Drop Calculator will allow you to calculate the voltage drop via your wiring.
This is what your link shows:
Insulated copper
strand 1-wire, 1x0,14mm²
multistranded (18x0,1mm)
material flexible
colour Gray
Dimensions
about 1.1 mm
cable length10 m
Electrical values
electricity 0.8 A
tension 100V
This is the max current 800mA * 12V = 9.6 Watts as the capacity of the wire at 12V. The power supply is as you state is 80 Watts. You need to check worse case current in each leg of the circuit. A trick to extend the switch life is put a ,1 cap across each switch with an inductive load such as the motors and the main.
For these parts of the circuit 0.14mm2 it should be fine: the first fan draws 200mA, the LEDs draw about 650mA and the last 2 fans draw approx. 400mA (200mA each).
It seems that the wire would be too thin for the power switch, power jacket and power to external cnc board right? It should be more like 0.6-0.8mm2 according to the reference page you provided for these connections?