1) Can I automatically receive an email from my Drupal website when new updates are available ?
2) Can Drupal automatically update itself ? Is this risky ?
You could set up a cron job that uses Drush to update Drupal, but any Update can break the website, it is risky to not test them beforehand.
How to keep up to date on security announcements It is strongly recommended that you always keep your Drupal site up to date with the very latest minor release available, to remove known security vulnerabilities and existing bugs. Here are some of the most common ways to stay informed:
Via your website: One of Drupal's core features is that it is able to check if you are running the very latest release of Drupal, and any installed modules and themes. Drupal.org is also able to send you an email as soon there is a new release out. To check if your installation is up to date: Drupal 7: First enable the core module Update manager (if you have previously disabled it), then go to Administer > Reports > Available updates Drupal 5 and 6: First enable the core module Update status (if you have previously disabled it), then go to Administer > Reports > Available updates For more details visit the Update manager module page.
By receiving Security Announcement emails from Drupal.org: You can find the "Security Announcements" box in the Edit > My Newsletters tab of your Drupal.org user account. Via the Security advisories page: You can also subscribe to the page's RSS feed.