(a) Sodium is a very reactive metal so it reacts vigorously with the oxygen of air and catches fire. It is kept immersed in kerosene oil to protect it from the action of oxygen, moisture and carbon dioxide of air and to prevent accidental fires.
(b) White phosphorus is kept immersed in water because it reacts spontaneously with oxygen of air to form phosphorus pentoxide but does not react with water.
(c) No, because sodium reacts vigorously with water to form sodium hydroxide and hydrogen.