To determine which compounds are soluble in water, we need to consider their ionic or molecular nature and the solubility rules for ionic compounds.

1. Cs2O (cesium oxide) is an ionic compound composed of the Cs+ cation and the O2- anion. Compounds containing alkali metal cations (Group 1) and oxide anions are generally soluble in water. Therefore, Cs2O is soluble in water.
2. CaS (calcium sulfide) is an ionic compound composed of the Ca2+ cation and the S2- anion. Compounds containing alkaline earth metal cations (Group 2) and sulfide anions are generally insoluble in water. Therefore, CaS is insoluble in water.
3. Al2S3 (aluminum sulfide) is an ionic compound composed of the Al3+ cation and the S2- anion. Compounds containing aluminum cations and sulfide anions are generally insoluble in water. Therefore, Al2S3 is insoluble in water.
4. Hg2Cl2 (mercuric chloride) is a molecular compound. It is slightly soluble in water due to its covalent nature and the presence of weak intermolecular forces.
5. NiO (nickel oxide) is an ionic compound composed of the Ni2+ cation and the O2- anion. Compounds containing transition metal cations and oxide anions are generally insoluble in water. Therefore, NiO is insoluble in water.

For the second question, when K2O (potassium oxide) reacts with water, it forms potassium hydroxide (KOH) as the base:

K2O(s) + H2O(l) → 2KOH(aq)

Therefore, the correct answer is KOH(aq).

For the third question, the anion that will form a precipitate with Ba2+ (barium ion) is SO42- (sulfate ion). Barium sulfate (BaSO4) is a highly insoluble salt and will precipitate out of the solution.

Therefore, the correct answer is SO42-.