Take this one step at a time.
First connect up the motors and switches one axis at a time and test fully for direction and limits switches both electronic in the CNC software and or as hardware switches.
Secondly connect the 'estop' switches as per Support.
Thirdly consider the mains isolation as a separate issue. The local health and safety rules are different for each region and there is some confusion over the terminology. The health and safety view is that the machine should stop as quickly as possible into a safe state so that the injured can be extracted with out causing additional harm to either the victim or those providing assistance. There are also recommendations on the sitting and type of switch used and in particular the restart.
The other view is the temporary stopping of the machine to permit moving of clamps and or tool changes due to breakage. The ideal is to stop the software chain of CNC commands to permit the work operation to resume - this is not practical in my opinion!
One solution - not necessarily the best - is to use the local red buttons as per the GECKO application notes and to provide the mains supply with a contactor (mains high current relay in the local fuse box) operated by multiple red buttons of the approved type at the various locations around the work area. This relay / contactor then removes all external power for all machines in the area but you must consider linking these two somewhat dissimilar stop systems if the individual machine continues to operate after the mains input power is removed. Large saws and hydraulic machines are but two examples where consideration of the run down time needs special consideration.
I use red buttons to isolate the workshop from the mains supply (not lighting!) with a key operated reset. I use the key to act as a reminder that the red buttons are for emergency stop not routine use. Each machine is also provided with its own start stop switches in convenient places for the operator. However I am not suggesting that this meets the safety requirements nor any legal responsibility to protect both the operator and any visitors and I would advise seeking out the local requirement for safe operation.
Last as to the switch terminals - just use a battery and bulb to discover the switch connections it is possible that there will be terminals that are not used and the switch may also only be low current / voltage which is why an auxiliary relay / contactor in the fuse box should be considered. I use the contactor as a no volt detector as my mains supply is reasonably free from breaks and glitches. The red button switch looks to be of standard design The red pair and green pair are separate switches and are of the normally open or normally closed change in state being effected by the possition to the switch which may / should latch in the pressed state and be released with a twist. The rotary switch is normally used as a manual control for the motor rotating the primary spindle not for CNC so I suggest this is not going to be part of the CNC side of the machine controls. I can't think of a suitable use for this switch nbut some one else may chip in with a suggestion.