Initialize WordPress environment to use in a real cron script

I have to run a PHP script through real cron (WP cron being too unreliable). Within that script, I need $wpdb to insert data into WordPress table. But of course $wpdb will not be available as WordPress would not be initialized. Right? So, my question is how to ‘include’ WordPress/initialize WordPress environment to do such tasks? How about
require_once(“wp-load.php”)?

How do I log plugin (cron) actions?

Is there a recommended way to log (failed) cron actions from your plugin? For example, I have a plugin that synchronizes with an external service every hour. I want to log how much was changed, but also when the synchronization failed. What would you recommend here? A new database table? The Log Deprecated Notices plugin does this with a custom post type, but this might be too much overhead? I believe WordPress does not come with a standard logging package?