Ok here goes but I take no responsibility if anything goes wrong and if you are not 100% sure about electrics I suggest you get help for someone who is more clued up. Because the manual is dodgy I would advise you to put a meter on the terminals to verify wires.

9 Pin connector first:

Pins 1 & 5: This the thermal sensor which is just a switch that changes state above a set temperature so you wire this in series with however you want it to report the high temp. This could be by turning a light on or sending a signal to the controller which can then show up as a fault.

Pins 3 & 9: This is a little obvious but it's the power for the Fan. Provide these wires with 12Vdc Red =12v(pin9) Black-0v(pin3)

Pins 4, 6, 8 are the main power from the VFD U V W

Pin 2 = Gnd

11Pin: This is a little trickier because your manual is rubbish and I've never fitted an air-cooled spindle like this one. But here's what I think.

Pin 6 = goes to Negative (0v) of 24V power supply which you'll need to power the drawbar sensors.
The Brown wire goes to the 24V+ side of the power supply. Don't know which pin this is on your spindle.

Pin 1 = Is the signal for drawbar closed or could call it tool holder in the spindle. This you would connect to an input of the controller so your tool change macro can monitor the input, it's a PNP switch so your controller must be able to handle PNP.

Pin 2 = Is the signal for drawbar open or No tool holder in the spindle. Connect the same as above

Pins 5, 11, 7, 8, I think go thru the Momentary switch so you can manually power the solenoid to release the tool.

The pneumatics you control using Outputs from your controller to switch on solenoids. You'll need 4 solenoids 2 for power drawbar, 1 for Air purge to clean the taper, 1 for air bearing while spindle runs keeping debris out of the bearings.

That's about all I can tell you from what you have shown me, carefully check the wiries to verify before connecting up.