Which reaction to use for standard formation enthalpy? What reaction illustrates $\Delta H^\circ_\mathrm f$ for $\ce{CaCO3}$? 


Answer: $\ce{Ca(s) + C(s) + 3/2O2(g) -&gt; CaCO3(s)}$.

Ok so why isn't it: $\ce{2Ca(s) + 2C(s) + 3O2(g) -&gt; 2CaCO3}$

Or

$\ce{Ca(s) + C(s) + O3(g) -&gt; CaCO3}$ ?

For example in another similar question:


  Choose the reaction that illustrates $\Delta H^\circ_\mathrm f$ for $\ce{Ca(NO3)2}$.


Answer: $\ce{Ca(s) + N2(g) + 3 O2(g) -&gt; Ca(NO3)2(s)}$ 

Can someone confirm this assumption of mine:  it's ok to use fractions in these types of equations to blance it out as long as it's in oxygen's coefficient.

As that assumption correct?
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.