Ok...
1. When you do "$this->mail_id = $mail_id;", you're referencing the same thing. $this->mail_id is used inside functions to reference the variables in the parent class. So, basically, your email() function is unneeded.
2. Also, if all you're doing is echoing your query, and not using mysql_query, then obviously you're not going to be doing any action is your database.
I think a much simpler way to do this, without classes, is:
function storedRecord($mail_id, $name, $phone, $senderName, $guestEmail, $guestPhone, $subject, $message) {
$sql="INSERT INTO emailrecord (name, phone, senderName, guestEmail, guestPhone, subject, message)
VALUES ('$name', '$phone', '$senderName', '$guestEmail', '$guestPhone', '$subject', '$message')";
$result = mysql_query($sql) or die(mysql_error());
return $result;
}