Which reaction to use for standard formation enthalpy?
The heat of formation refers to the formation of one mole of the compound from its elements in their natural states at $1\mathrm{~atm}$ and $298\mathrm{~K}$.  Your first example forms 2 moles and your second example uses ozone, which is not the "natural state" of oxygen at $298\mathrm{~K}$ and $1\mathrm{~atm}$.

Regarding your question about oxygen, it has nothing to do specifically with oxygen. The important thing is to have 1 mole of the compound on the right hand side of the equation.