Why is that doctors advise not to drink water right after an operation?

Due to administration of anaestheia (be it general anaesthesia in which patient is completely unconscious or regional in which the patient is awake and only a part to be operated is anaesthetized) the patient is asked prior to operation or after the operation not to consume any fluid or food, so as to avoid a deadly complication of any risk of aspiration into the lungs.

Due to fasting the patient has empty stomach, so the risk of aspiration is reduced. During operation patient is also administered  sedatives and anxiolytics, which may have a residual effect for some time after operation, which alters the active airway reflexes of patient. Nausea vomiting is a common manifestation after operation as a side effect drugs and inhalation agents used for sedation. So initially patient is started with only light food and fluids post operation after prescribed hours for both. Thus the main reasons are to avoid vomiting, and ensure rest to bowels.

How drinking soda helps us during indigestion?

Soda or carbonated water is water in which low levels of pressurized carbon dioxide has been dissolved, thus creating carbonic acid. Soda water causes bloating, which stretches the stomach. Mechanoreceptors in the stomach detect the stretching resulting in parasympathetic innervations to gastrointestinal (GI) smooth muscles. This results in an increase in GI motility.

Since soda water is in a liquid form and thus easily passes down the oesophagus and the lower oesophageal sphincter relaxes and opens to allow its entrance into the stomach. The upper part of stomach relaxes to store the swallowed soda water. The digestive glands in the stomach lining produce hydrochloric acid, containing pepsin. Stomach mixes the digestive juices with soda water. Upon reaching the small intestine, soda water mixes with secretions produced by the pancreas and liver.

When the stomach is empty, soda water passes rapidly in to the duodenum where carbon dioxide is transformed into bicarbonate. The carbon dioxide dissolved is rapidly released in gaseous form as the fluid is warmed. The free carbon dioxide may be belched if the expanding gas increases the pressure and stimulates the gastric fundus, triggering the belching mechanism. Distention of gastric fundus can increase transient lower oesophageal sphincter relaxation. If the soda water is taken while or after eating it tends to localize in the upper part of stomach and will produce feeling of fullness. Hence, carbonated water seems to influence stomach function by both mechanical and chemical effects.