Not all ionic substances can dissolve in water; and save for a few exceptions, it is a known rule that any ionic compound that contains carbonate, oxide or hydroxide anions are insoluble in water. Barium Sulfate, Calcium Sulfate and Lead || Sulfate are just few of these examples.
Statement 2 is false, as once again a generalization is made.
The most common examples to take to refute this claim are Sugar and Ethanol. They are both covalent compounds, but they dissolve in water due to their hydroxyl groups.
Statement 3 is true.
The addition of heat facilitates the reaction by supplying energy to break the bonds in the solid and so most commonly, an increase in temperature produces increased solubility in solids.