Question

Anybody knows about documentation or examples that how copy files (workspaces,shapes,..) in geoserver usinG C#?

Answer 1

This C# code will create a new workspace on GeoServer.

using System;
using System.Net;
using System.IO;

...

string url = "http://localhost:8080/geoserver/rest/workspaces";
WebRequest request = WebRequest.Create(url);

request.ContentType = "text/xml";
request.Method = "POST";
request.Credentials = new NetworkCredential("admin", "geoserver");

byte[] buffer = Encoding.GetEncoding("UTF-8").GetBytes("<workspace><name>my_workspace</name></workspace>");
Stream reqstr = request.GetRequestStream();
reqstr.Write(buffer, 0, buffer.Length);
reqstr.Close();

WebResponse response = request.GetResponse();

...

GeoServer has examples on how to do create workspaces, stores, layers and styles using cURL: GeoServer cURL REST Configuration Examples.
Then you can convert the cURL examples using the code above.