Oxygen installs as a plugin, not a theme. Install Oxygen and all add-ons from the Plugins > Add New > Upload page of your WP admin.

Enter your license keys at Oxygen > License to get one-click updates from your WordPress admin panel.

Please note that you need to enter your Oxygen key, not your Oxygen Pro key. Your Oxygen Pro key does not need to be entered anywhere.

There is no downloadable file for the Components & Design Sets. Simply enter your license key for the Components & Design Sets on the Oxygen -> License screen, and they will automatically appear in the Add+ section of Oxygen.