You can sideload the Gmail app, and most other Google apps, if you sideload and install the Google Services Framework prior to installing the Google apps.
I currently have Gmail running on my un-rooted Kindle Fire with no problems.
Same here. Just download the Google Services Framework (Google it), then install Google books, reboot. Open Books, add your Google account.
Sideload other Google apps> Gmail, GDocs, Google Play Books, Google Earth, Google Reader, Google+, all work well. Couldn't get Google Music to work.