I have set up my domain with windows live, now If I add an alias to the primary email that I used to sign up, a message tell me that a link has been sent to the alias email, in order to verify that I own the alias email. My problem here, the alias email does not exist, any way to add an alias email to my custom domain without sending a verification?
By sending an email to the alias, the verification email is supposed to arrive at your original mailbox.
An alias is not a new email identity - it's another name ('alias') you call your existing one. This way, you can give different sites/people different aliases, and thus hide your true email address, and see who's sending you what (great for catching spammers).
Bottom line: after creating the alias, look in your original mailbox.