I agree on Rocket Loader. It’s not that compatible with a few things, and really doesn’t buy me much performance increase, so I very rarely use it.
Your site behaves as if there are HTTP/S issues. I also see that you have NGINX server caching enabled. That may also be conflicting with Cloudflare’s cache. I suggest that you turn it off…for now.
I strongly suggest that you use the “Pause Cloudflare on Site” option from the lower right corner of the Overview page. Then wait five minutes for that to take effect.
Go through your site and make sure that everything is configured to load over HTTPS.
Once your site loads perfectly with HTTPS, go back to the Cloudflare Dashboard: Make sure SSL/TLS is set to Full (Strict). Then Un-Pause Cloudflare from the Overview page.