Is shopping on this website safe? 

Yes.  All sensitive data is protected by a Secure Socket Layer Certificate.  Security testing is provided by Security Metrics and Verisign.

How can security be verified?

Check the secure lock icon.  A closed lock means the site being viewed is using encryption. You can double-click the lock icon to display the security certificate for the site. 

When you check the certificate, the name following issued to should match the site you are on.

Why does my address bar now say https://www.storesonlinepro.com?

This website uses a certificate file through it's hosting company, StoresOnline, Inc.  When secure information is sent (such as credit cards), it is done through the this website's hosting company where the certificate is located.  After all secure data has been sent the visitor is then sent back to the original website.