You will not need to disable the core "Email Cloaking" plugin, as Email Protector will automatically disable the Joomla core plugin on installation.
Note: However, the core email cloaking plugin will not get re-enabled automatically if you uninstall Email Protector.
When you use the Inspect / Inspect Element console in your browser, you will be presented with the html structure (DOM) of that particular moment. That is not the actual html output your website generates. So you see the email address because Email Protector converts the cloaked code to a visible email address after the browser has loaded the page. This is fine and safe.
To see the actual html output of your site, you need to use the View Page Source option in your browser. You will see that here, the email address is indeed protected/cloaked.
There is no Pro version of Email Protector. It is completely free!