Woocommerce has had a big update recently. So it is no wonder that there are major changes in it’s code that will affect the email work.
I can suggest to, first copy once again the file woocommerce/emails/customer-completed-order.php from a newly updated woocommerce plugin folder (make sure it’s the latest version of plugin). And then redo the changes you have made to customize email template. Save a copy of the current version of the file as backup, in order to always have where to find the changes made.
Sorry but this is not related to theme question. It seems you have registered the main domain name as site.com/blog. If you made the changes of domain correctly then perhaps clearing cache of wordpress and server will help reflect the changes sooner.
Or check your database for in case there still is present the old url in any records.
Contact your host for more regarding it.
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Please fill in the wp login information of the problematic installation on the extra information fields of your profile data. So we can give it a closer look.
