Driving bicolor LED from one I/O via 74HC595 shift register

Smajdalf:
The pin of Arduino that is driving clock signal needs to drive 45 inputs of 595s. It is too much for single Arduino's pin - it cannot do nice clean edges on such load with speed needed. This is reason for buffer - the pin is driving only a few inputs of 125s and the buffer drives only few inputs of 595s.

Ok, that's starting to make sense, so it's being used as a serial buffer. What are the calculations / specs used to determine how many 125s a single MCU pin can drive and likewise, how many 595s can be driven off the 125s.

I am yet to start playing with shift registers but I thought the point was that they are daisy chained off of each other thus reducing the I/O pin count required.

Is it only the CS pin that goes via the 125s or are the latch and data pins pushed through the 125 as well ?