How do I identify how many reactions are occurring when precipitating a mixture?
You asked two very different questions.


  (1) How do I identify how many reactions are occurring when precipitating a mixture?


There is no information in way the reactants are shown in a chemical equation as to what the products will be. That is to say that you have to know the products of the reaction. 


  (2) For this one, would the reaction be two equations?


Chemists use shorthand all the time. Reactions are typically netted out to the pertinent aspect under consideration. However if I were writing the reactions for the second problem I'd do it much differently that you have presented. I think I'd write:

\begin{align}
x\ce{CaCl2} + y\ce{RbCl &amp;-&gt;} x\ce{Ca^2+} + y\ce{Rb+} + (x+y)\ce{Cl-}\\
x\ce{Ca^2+} + y\ce{Rb+} + (x+y)\ce{Cl-} &amp;\ce{-&gt;[excess AgNO3]} x\ce{Ca^2+} + y\ce{Rb+} + (x+y)\ce{AgCl v}\\
\end{align}

From an analytical chemistry perspective there are two steps. First the chloride salts are dissolved and then the silver nitrate is added. You wouldn't want to add the salts to a silver nitrate solution since the silver chloride could coat the Ca and Rb salts preventing a complete reaction. 

I even might write the second reaction as:

$$ (x+y)\ce{Cl-} \ce{-&gt;[excess AgNO3]} (x+y)\ce{AgCl v}$$

I'm not a fan of one line jobs like:

$$x\ce{CaCl2} + y\ce{RbCl -&gt;} x\ce{Ca^2+} + y\ce{Rb+} + (x+y)\ce{Cl-} \ce{-&gt;[excess AgNO3]} (x+y)\ce{AgCl v}$$