Why do we see the limestone on top of Cambrian layer?
No.  CaO will not exist in most environments for any significant time in the presence of CO2, it will react to form CaCO3.  I doubt CaO is the primary source of Ca in our world.  Silicates are likely the original source of Ca in our oceans https://en.wikipedia.org/wiki/Silicate_minerals.  CaCO3 will partially dissolve or corrode in water to form an aqueous solution of Ca +2 + 2 HCO3 -.  The dissolution of the CaCO3 in water is an equilibrium reaction based on the acidity and temperature of the water, this is why the acidification of the oceans is a concern for our marine life.  I am not a chemist or a biologist but organisms will extract the aqueous Ca +2 ions found in the water to form shells etc.  Because these organisms are not evenly distributed in the ocean their shells and skeletons will and have accumulated the CaCO3 in distinct areas.