The reason a booking page URL has our domain name in it, is because the booking process is part of the PromoteMyPlace application, not your website. Although we match the look and feel of your website, so it's not so obvious. This is the same way it would work with other booking software, such as SuperControl.
And the booking email comes from email@example.com, because the email is being sent from our application. It's not possible for us to send email from your email address, if it were, that would mean that anyone could hijack your email account. However, the display name on the email should be yours and if the guest clicks reply, the reply will go directly to your email address.