What can be used to distinguish a carbonate from a hydrogen carbonate?

Answer 1

Phenolphthalein indicator will distinguish between Na2CO3 and NaHCO3.
CaCO3 is not soluble in water but Ca(HCO3)2 is soluble.
I think that there is no general rule for a simple test that will distinguish between carbonates and bicarbonates. However, if you know which bicarbonate and carbonate you are distinguishing between, as in the two examples above, a simple can usually be found. If not looking for a simple test, one can always titrate the unknown but this is not a simple test.