How to Create Yahoo/Gmail Account from my windows Application?

The only thing that you can do is using Google, Microsoft, Facebook or Yahoo as Identity provider in order to authenticate users. So , if it's the case refer to WIF(Windows Identity Foundation)

You can't register by using program, so called "bot" in internet world.
Only human can register it.
There is a captcha system which is designed only readable by human.
However, you can try to write a program that can read the captcha image, of course.

I remember doing something similar few years back. I implemented a WebBrowser Control, thereby loading the Website (Sign up page in your case) inside that.

Then use WebBrowser.DocumentCompleted Event[^], which gets fired when the document is fully loaded.

Now, you can loop through all the controls in the page and assign values to them.

HtmlElementCollection theElementCollection = yourWebBrowserControl.Document.GetElementsByTagName("input");

foreach (HtmlElement curElement in theElementCollection)
{
    string controlId = curElement.GetAttribute("id").ToString();

    if (controlId == "Email")
    {
        curElement.SetAttribute("Value", "someEmail@abc.com");
    }
}

Here it is looping through all the controls, finds the Email field by its Id and assigning value to that.