Hey David,
welcome to the world of pneumatics! You will now have to get into this new matter a bit in order to know how to attach this and make it run.
A spindle that supports sealing air will live much longer, since it is impossible that dust comes into the spindle. Tom @TMToronto connected one more recently than I 
The connector on the right is for a one-hand quick-release ISO 4414 connector that you find on air compressor hoses. See this article in Fluid Power Journal.
The maintenance unit is explained here: Festo MS4-LFR. What you can let out is condensed water at (E).
The air solenoid valve Festo MHJ10-S-0,35-QS-4-MF switches the sealing air on and off by a relay which you can be controlled by your VFD just like it controls water coolant pump. Yes black is BK, blue is BU and BN is brown.
All hose connectors are tool-less Festo QS system.
Yes, the piece end (C2) goes to spindle openening (D). This is the input for the sealing air. You should be able to spin the hexagonal nut on the L piece, is this not the case? It should look like on this spindle when mounted.
Please don’t buy one of these oilless compressors or you will service it once a year.
Recently there was a good article in german Make Magazine about Pneumatics for CNC users. Not only you can have spinde sealing air and automatic tool change control with it but you also control pneumatic actuators with it e.g. to clamp your workpieces. In the article, they suggested the encapsulated oil bath compressors from Jun-Air (formerly Blue-Air) (EU, US). They are quite expensive but extremely silent and service-free. They look and work like the encapsulated oil bath compressors that everyone knows from refrigerators, which are also very silent and service-free.