CaCO3 and NaHCO3 effect pH in similar ways, Calcium Carbonate is the stronger alkaline buffer though because it can pick up 2 H+ where as bicarb alread has an H+. Both can form bicarbonate ions depending on the pH.
This is myth, Ca actually can reduce kidney stones while Na increases the probability they will develop. Ca could have negative cardiac effects above 1200mg per day though.
But sodium bicarbonate is a standard medical treatment for acid stomach or reflux. They even have it in pill form.