You can check integrity of files by SHA1 hashes. It also signed by OpenPGP key of t_mrc-ct[at]users.sourceforge.jp. The public key could get from here or OpenPGP Keysever.
Auto Updater does not fully supported. (Update Checker is supported. But you should download and install new version manually.)
From 17.0, Tenfourbird doesn't contains Enigmail add-on. It provide separately. Enigmail for Tenfourbird 10.0.* or before does not automatically update. You should manually download and install Enigmail for Tenfourbird 17.0.* or later.