With reference to the LP Comparator AC Specifications, in low power mode, response time of 38ns indicates that when the overdrive voltage is 50mV (that is difference input at op-amp input) then the response time from input to output will be 38ns.
The same holds good for both low power and ultra low power mode also.
If the overdrive voltage is less than 50mV then correspondingly the response time increases. Hence as the overdrive voltage reduces the response time increases.
The minimum difference voltage the comparator may detect depends on the stability of the input signals.
Consider the input and reference voltage is very stable. If hysteresis is enabled, it will increase the reference voltage by 10mV. This is to avoid the variation in voltage because of noise and get undesired output. This also infers that the comparator can detect the change as small as 10mV. But the corresponding response time will be increase.