How to get the xml node value in string

You should use .Load and not .LoadXML

MSDN Link

"The LoadXml method is for loading an XML string directly. You want to use the Load method instead."

ref : Link

The problem in your code is xml.LoadXml(filePath);

LoadXml method take parameter as xml data not the xml file path

Try this code

   string xmlFile = File.ReadAllText(@"D:\Work_Time_Calculator\10-07-2013.xml");
                XmlDocument xmldoc = new XmlDocument();
                xmldoc.LoadXml(xmlFile);
                XmlNodeList nodeList = xmldoc.GetElementsByTagName("Short_Fall");
                string Short_Fall=string.Empty;
                foreach (XmlNode node in nodeList)
                {
                    Short_Fall = node.InnerText;
                }

Edit

Seeing the last edit of your question i found the solution,

Just replace the below 2 lines

XmlNode node = xml.SelectSingleNode("/Data[@*]/Short_Fall");
string id = node["Short_Fall"].InnerText; // Exception occurs here ("Object reference not set to an instance of an object.")

with

string id = xml.SelectSingleNode("Data/Short_Fall").InnerText;

It should solve your problem or you can use the solution i provided earlier.