Yes, the page is a simple template and you can override it by putting the file template “fbanner.php” inside the theme folder. You can also customize the style by adding your custom CSS in the specific option of the settings.
Yes, you simply leave the “Name” field label empty to achieve this.
No, you can also deactivate the footer banner if the plugin is active.
You can follow instructions on this tutorial to connect it to MailChimp email provider.