Switch off the site from public access. Then switch off all third parties applications and plugins. Then switch on the default theme and try. Then if it is working, try to switch on applicatiuons and plugins one by one. If it is still working then try to renew the third party theme up to the site version.
"So , how can disable guest orders ?"
It is not possible do set permission on Checkout for any group. So, either you disable the Shop from Guests, or you disable any particular product from being displayed to Guests.
"I know in older version of IPS we had the option of a Trash Can, but we don't have that anymore."
Is it not working on 4.4.2? https://www.yoursite.com/modcp/deleted/
Question 2: check the Moderators permissions (add your administrator member or Administrator group to Moderators here if not added). Also check Administrators section if you are added there or not.
This means that your server lacks of resources. If you have SSH access then login to the server and try the top command. You will see how it is doing at the moment.