I think you're mistaken on #2. The point of using a zener diode is that, like a voltage regulator, its 'regulated output' stays relatively constant, as long as the input voltage is higher than the breakdown voltage of the zener diode. Such diodes are frequently used in voltage reference circuits. Some comparators also include voltage references to make them easier to use and less prone to the very issue you raise.
So, creating a stable power supply is not as much an issue of whether it can be done, but at what cost (in terms of component cost vs. power consumption, vs. board space vs. temperature stability, etc.). So a zener approach might work well, but I'd seriously consider a comparator with an internal reference first - the power consumption is likely lower. Simply head over to digikey, search for a linear comparator, and filter for units with built-in voltage references. The least expensive (SOIC) single channel unit is around $0.50 (TSM931-TSM934). THrough hole versions (DIP) that work well in breadboards start around $2.75.
Cheers.