Point one is a general statement and does not indicate the "how" of how HHO improves the combustion.
Point two is true, but you would need in the order of tens of kilograms of carbon in your combustion chamber to effect an improvement of mileage over any significant amount of time, and water (steam) has more to do with the carbon deposits than does the HHO.
Then, you come to the conclusion that your O2 sensor reads more O2 in the exhaust when you add HHO. Which the above tests do NOT prove. Your salient points do not logically support your conclusion.
Restate your conclusion so as to be supported by your research points.