Wiring a ceiling fan with black, white, red, green in ceiling box and two wall switches
That's not really a white wire coming out of your fan control

When the instructions for your fan control say a wire is "black/white" -- they mean it's a black wire with white stripes on it, which has nothing to do with the white neutral wires in your box.  

As to wiring up the fan control...

The new fan control gets wired as follows, then:


Green gets nutted in with the rest of the greens
Black/white gets nutted to the bundle of red wires that the two bottom black wires came off of (the two bottom black pigtails can be removed and saved for use down the road)
Black gets nutted to the black that was nutted to the top right black pigtail
And blue gets nutted to the red that was nutted to the top left black pigtail


You'll also need a two-gang faceplate that has a decorator opening on one side and a blank space on the other -- either that, or a decorator opening blank for your existing faceplate, considering that the new control only takes up a single gang of box space.

And to the fan itself

The fan, though, is a bit easier to wire:


Ceiling red to fan blue
Ceiling black to fan black
Ceiling white to fan orange and white
Ceiling green bundle to fan green


As to mounting that fan...

Your box is likely a special type of box known as a concrete box that was poured right into the ceiling.  This type of box, however, does not have the correct setup for mounting a fan to it (the mounting ears will bend if you try, letting the fan fall on your head).  So, you'll need to use masonry fasteners to mount the fan to the concrete surrounding the box, instead.