Will Composer and Drush be mandatory in future Drupal releases? If so, I think Drupal will not be an option for non-programmers in the future.
Composer or Drush are not required to install / manage Drupal 8. When downloading tar / zip core from the Drupal office website, you can install it manually.
When I manually update Core, I think the provider folder, autoload.php, composer.json and composer.lock will be updated in the tar / zip files. So, does it make any difference to use Composer for this task?
Yes for composer.json or composer.lock. Because if you want to use Composer to update core, you will also manage contribution modules (with version) in composer.json and drupal core.
You can view more details in Update core manually
I have come across a contributed module that requires installation using Composer. Can I install / update this particular module with Composer without converting the entire site to manage it with Composer?
For the contributed module that requires installation using Composer, I believe that the module will also have the manual way to install / update (downloading tar / zip files and relationship libraries, replace the existing module to update).
I don't think you have the way to install / update the particular module without converting the entire site that will be managed if you use Composer, except that the module is managed by the composer himself (composer.json and composer.lock in the module) and you You need to run composer within this particular module.