Hi Don, yes sure. To check your orders you log into the WordPress dashboard and click on 'WooCommerce' and then 'Orders' and it will then have a list of all your orders and then you can click on number to view and edit order status.
In terms of why you're not getting the email notifications from WooCommerce are you getting other email notifications from the site (maybe test a password reset just to see if emails are being sent)? I'd then double check the email address you have listed 'Settings' and 'General' as the site admin as that is what it will use by default. Alternatively you can also nominate email recipients by going to 'WooCommerce' and then 'Settings' and then select the 'Emails' tab and then select the 'New Order' link for example and you'll then see a field to enter a recipient email address.
I'd also make sure that you've backed up the site recently and then check you've applied the latest updates to make sure there is nothing funny going on there. Hope that helps - let me know how you go