Author URI: http://www.fiftyandfifty.org/ Purge your entire CloudFlare cache from within WordPress.
Yes, setting up a CloudFlare account is free and can take less than 5 minutes.
= Does it purge anything on page/post creation?
Yes, if you set 'Auto Purge on Update' in the admin it will fire on WordPress' 'publish' hook which includes new pages/posts. Typically the page/post url won't exist in you CloudFlare cache yet so just the homepage would get purged.
= If you set posts/pages to auto-purge on add/update, does the homepage URL get purged as well?
Yes, we assume that you have a blogroll that would need to be updated on the homepage.
= Are any other URLs purged automatically if I set 'Auto Purge on Update'?
No, just the page/post permalink & the homepage. You would have to manually purge any other pages that need to get updated.