The correct chemical reactions for the processes described would be:

CaO + H2O → Ca(OH)2 (Calcium oxide reacts with water to form calcium hydroxide)
Ca(OH)2 + SO2 → CaSO3 + H2O (Calcium hydroxide reacts with sulfur dioxide to form calcium sulfite and water)
CaSO3 + 2HCl → CaCl2 + H2O + SO2 (Calcium sulfite reacts with hydrochloric acid to form calcium chloride, water, and sulfur dioxide)