What versions from the Symfony components are used from core? Which Symfony version does Drupal use for the Symfony components? Is it a goal to support the latest versions of the components or is this simply not possible?
It is more accurate to say that Drupal 8 uses Symfony components, rather than all of Symfony.  If you look at 'core/composer.json' you will see all of the individual components that Drupal uses listed out.  The precise versions that get installed are listed in the 'composer.lock' file.

Drupal 8.2.x uses the 2.8 versions of these components.

For Drupal 8.3.x, there are issues open for updating to 3.1 and 3.2, but these are still works in progress. (I think there may be a 3.3 issue, but I can't find it).

The goal is to start tracking the 3.x versions, but the conversion has not been straightforward.