That's because in the "Registration" option of the Checkout tab of the configuration, you don't have "Registration" selected. Change that and these fields will appear.
Do you get other emails on your website ? Joomla emails ? HikaShop order emails ? If not, it might be because the email settings are not correct and you should seek advice to your hosting company regarding the correct email settings for your website.
If yes, then check your spam box and if you use the business edition, check that the user account email is published via the menu System>Emails.