I have one mySQL database and one Apache webserver. Can I still run 2 separate wordpress/Civicrm environments (like staging and production)?
Yes, you can have multiple Civi/CMS instances on the same server. Depending on your preference, when looking at your server, you will see something along the lines of one of the the following structure:
Per comment - editing my response to include database - unless you are setting up a multi-site instance of Civi, you would need a separate database for each CMS instance.