Template Problem if Google PageSpeed plugin is not disabled

Thanks, I'm a new Firecoders user.
I'm running Joomla 3.8.6 and Gantry 5 Framework. I installed Route 66. When I try to put my site online, and I browse the homepage without logging in, I have some problems with the template: text font not loaded correctly, Gantry particles that do not work properly.
If I view the site by logging in, however, everything works fine.
If I disable the System - Route 66 Google PageSpeed plugin, all works, and the template is regularly loaded.

I'm using Medical template, developed by Inspitheme. If I exclude Gantry 5 Theme (but only in the home page), all works fine, but I get Low 44 / 100 in PageSpeed Insight.

In addition to this, in all menu items that belong to the sublevel, I do not see the image "Intro Image" of the category. The image in the Blog view is not loaded because Joomla looks for the image in an incorrect location.