Drush 8 should work just fine with remote sites running Drush 7.
To get around the error message you are seeing, run
composer install from the Drush directory.
If you want to install multiple versions of Drush to run locally, the easiest way to do it is to manage your Drupal site with Composer, and add a 'require drush' line in your composer.json. If your global Drush is at least version 7, then you will find that Drush automatically dispatches to the site-local Drush whenever you target it.
One really good use-case for doing this would be to run Drush 7 stable as your global Drush, but use Drush 8 with any Drupal 8 site.