calling java web service "REST" that require auth with username & password and certificate from .Net C#

You can consume a webservice without a WSDL by sending a POST request with the WebClient, and filling the body of the request with the SOAP XML message.

You might need to add additional HTTP headers. First do a request with SOAP UI and look at the request with fiddler. Then send the request with WebClient. The code should be similar to this:

using (var client = new WebClient())
{
    // this is the string containing the soap message
    var data = File.ReadAllText("request.xml");
    // HTTP header. set it to the identical working example you monitor with fiddler from SOAP UI
    client.Headers.Add("Content-Type", "text/xml;charset=utf-8");
    // HTTP header. set it to the identical working example you monitor with fiddler from SOAP UI 
    client.Headers.Add("SOAPAction", "\"http://tempuri.org/ITestWcfService/TestMethod\"");
    // add/modify additional HTTP headers to make the request identical with what you get when calling from SOAP UI on a successful call 
    try
    {
        var response = client.UploadString("http://localhost:8080/TestWcfService", data);
    }
    catch (Exception e)
    {
        // handle exception                        
    }
}

I'm not sure about the certificate, but maybe you can set it to the web client too somehow. Unfortunately, I don't know much about client certificates. But if you can explain in comments I might be able to help you. If you manage to make it work using this solution, please also post here your additional work to handle the certificate problem.

WebClient is the class from System.Net in System.dll assembly.