Icons in buttons are missing/give a strange (other) icon

After copying my website to our public webhost (from test directory to default root dir) some the build-in icons suddenly won’t appear. With build-in icons I mean the icons that I used in contact buttons. The same thing applies to the mobile responsive menu icon in the top of the right. As well other JavaScript buttons, like the button to go to the top of the page (also currently visible on this page on the right under) result in a strange icon. Technically the functions are working properly.
I already tried cleaning my cache, using different browsers (Firefox, Chrome) and use different devices.

Please help me out. We would like to make our site public this Saturday.