does a reaction occur when aqueous solutions of sodium sulfate and potassium carbonate are combined

Answer 1

NO. The reason being is that all reactants and products are soluble (aqueous) and are also strong electrolytes, so they ionize/dissociate completely..

Na₂SO₄(aq) + K₂CO₃(aq) ==> Na₂CO₃(aq) + K₂SO₄(aq)

If you look at the complete ionic equation you will see that all the ions are the same on left and right side. They are all just spectators and no reaction has taken place.