In ASP.NET the Page class exposes a Request property which provides access to a QueryString property - this is a NameValueCollection that lets you get values out in much the same way as in your existing example, by specifying keys:
var id = Page.Request.QueryString("id");
var newQuery = string.Format("?member_id=15893&id={0}&", id);
The above can easily be expanded to build more into your required query string.
As for the request you're initiating, that can be achieved using a WebRequest instance; to alter the sample from MSDN only slightly, here is an example:
WebRequest request = WebRequest.Create(yourUrl + newQuery);
HttpWebResponse response = (HttpWebResponse)request.GetResponse();
Response.Write(response.StatusDescription);
Stream dataStream = response.GetResponseStream();
StreamReader reader = new StreamReader (dataStream);
string responseFromServer = reader.ReadToEnd();
Response.Write(responseFromServer);
reader.Close();
dataStream.Close();
response.Close();