I have the following dialog form :
-
To get the submit button work put it inside the form.
However, this adds an unexpected margin at the bottom of the modal. Bootstrap 2.0.2 introduced the modal-form class to fix this or you can fix it yourself with a style definition like:
.modal > form {
margin-bottom: 0;
}
For linking to another page when closing the modal I go along with TheShellfishMeme
As for the × that is supposed to link to the homepage, why not just remove the data-dismiss='modal' and make it act like a normal link using a standard href='home.html'.