Output datatable to XML string
System.IO.StringWriter writer = new System.IO.StringWriter();
dataTable.WriteXml(writer, XmlWriteMode.WriteSchema, false);
string xmlFromDataTable = writer.ToString();

Use XmlWriteMode.WriteSchema to include the schema in the output.
 

Read XML into a dataset from an XML string
string strXML = "valid XML here";
System.IO.StringReader sr = new System.IO.StringReader(strXML);
System.Xml.XmlTextReader xr = new System.Xml.XmlTextReader ( sr );
DataSet ds = new DataSet();
ds.ReadXml(xr);