Hi,
If the page is processing without stopping, it indicates that your website is trying to contact another server and the other server is not replying to your website.
This can happen sometimes with email sending, but it can also happen with plugins connecting to their corresponding server.
I suppose this was not always the case on your website, right ? If so, did you recently add /configure a plugin which would do something after an order is created on your website ? This would be a prime suspect.
Are emails still being sent by your website ? You can first use the "send test email" button of the Joomla configuration page in order to check this. If this email is not sent, then it means there is a problem with the connection to the email server and you'll have to check with your hosting what's going on.
Also, is the order being created if you check your orders listing in the backend ?
Do you see the emails corresponding to the order in the Customers>Emails history menu of HikaShop ?
Also, the PHP error log of your server might contain a fatal error message about this. So I would recommend looking into it. This could provide precious information about what is going on.