What is the highest pulse rate possible using PIC12F683 measuring the period of a square wave
The Fine Manual is your friend.
Since you're using the Capture-Compare Module, you'll need to look for its AC Electrical specs, and you'll find these on page 131.
There you'll find a formula for the minimum CCP1 input period. This formula tells you that it depends on the PIC's instruction clock period (Tcy) and the CCP prescaler setting (N).
Since that PIC has a maximum clock frequency of 20MHz (or a minimum instruction period of 200nSec - remember those PICs divide the oscillator frequency by 4 to get their instruction clock), the maximum frequency you should try to measure with the CCP (set to a x16 prescaler) is 25MHz (or a period of 40nSec).