Is it possible to fork current Drupal installation for experiments and have two versions of Drupal with one installation of Apache, PHP and MySQL on Ubuntu?
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Yes; See the handbook page on drupal.org: Installing virtual hosts for Drupal sites and subsites.
You can install two instances of Drupal in different sub-directories of the Server root directory; when you install them, you need to use different databases, or a different prefix for the tables used from each Drupal installation.
Doing so, I was able to have an instance of Drupal 5, two instances of Drupal 6, and two instances of Drupal 7 in my test computer.