I've never tried "serious" fasting, meaning a fast of several or more days.
But conserning the "empty stomach" - for me personally it is important to have the stomach empty BUT not depleated of energy. Meaning - I don't consume solid food before static, but I do make sure I have enough energy (gatorade etc).
I think the biggest benefit from morning statics without breakfast is that you respiratory quotient is lower. Basically before breakfast you are in pure fat metabolism, but once you eat, carbohydrates will be used which increases your RQ (more co2 produced per oxygen used). Meaning, the breathing reflex will activate later/weaker. I don't think it has much to do with oxygen - ie absolute limit, simply it is more comfortable. This is usually beneficial for static, but I must stress that I don't consider it at all beneficial for DYN/CW disciplines, where you really need the energy.
There might be a marginal effect from "empty stomach" in the fact that the less space your intestines take, the more air you can (comfortably) fit in your chest cavity
Having contractions on full stomach is just unbearable - and has...uh, side effects in the very end of the digestive system.
I guess it's generally accepted that before static a good general rule is 3-4 hours between last meal and the static, and the last meal is not very heavy. For competitions I stop solid food the previous night.
The idea behind a longer fast is that you would slow down you whole metabolism and thus increase also the total time (lower oxygen consumption). But like I said I haven't tried it and to my knowledge not many have with success. The most famous exception would be Sam Still who's said to have reached around 10 minutes with fasting, but details of his fast are a mystery to me.