I have two Questions I need help with.

Question

1. Why do some combinations of ionic compounds form a precipitate while other ionic compounds don't?
AND
2. Solutions of lead(II)nitrate and potassium iodide are combined in a test tube and form a yellow precipitate. What is the molecular equation for this reaction?

Well, a look around my pasture tells me that most ionic substances are not soluble. I have a lot of limestone here. Some are soluble, notably, Alkaline metals , and nitrates.
Solubility has to do with energy. These ions are attracted to water ions, or water polar ends, and when in the vicinity, release energy. If that energy is greater than the energy binding the ionic compound, then the compound breaks apart and dissolves as ions. If not, it is a precipitate.

Lead(II) iodide is an example of the internal binding energy being greater than the hydration energy.

Pb(NO₃)₂(aq) + KI(aq) ==> PbI₂(s) + KNO₃(aq)

You balance