Yes and yes. What we call gasoline is a pretty complex mixture of components. Sometimes the effect of one component or property is not straight forward.... But I think we agree the basic point about density is generally correct.

The Octane listed on the pump is just the Anti-knock number, not a component of the fuel. This is why octane can exceed 100, its not a percentage. In the USA the number is the Anti-knock Index (AKI) which is the average of two octane tests. These are tests against a mix of two fuels; one with octane ratings of 0 (heptane) and the other 100 (isooctane). see Chevron's Motor Gas Tech linked here

Oxygenated blends tend to be less dense and therefore lower BTU. But if the engine can use the oxygenates well, it may produce more power.

A wide band oxygen sensor is an indirect method of measuring AFR. If there is a question about density, then it is better use the lambda number rather than an AFR number. The AFR is based on an assumed stoich, and the stoich varies with composition and density. Suppliers of racing fuels publish stoich and density.
examples:
VP Master Fuel Table
Sunoco Race Fuels Comparison Chart

Street fuels are more difficult to deal with because their properties vary so much. As pointed out, most regions of the country have winter and summer blends. Automotive fuels throughout the country also have regional requirements due to climate as well as regulation. The suppliers need to stay within those requirements, but that can allow quite some latititude.