I've tried waybar with both the Font Awesome packaged under Ubuntu/Debian (confusingly called 5.0.10+really4.7.0) as well as 5.8.2 downloaded from the website as well as current git master from here:
https://github.com/FortAwesome/Font-Awesome/tree/master/otfs
All of them result in missing icons replaced by weird accented letters. Here's an example of how the config file renders with FontAwesome as downloaded from the website (version 5.8.2):

Thanks for posting your solution. Putting the FontAwesome font at the end works better for me, though; when it's at the front, all text is displayed using FontAwesome.
Got this, too. Is there another solution?
I don't know if this applies to all distributions, but you can also add the fix in /etc/xdg/waybar/style.css (saving the need to modify the source).
Most helpful comment
Thanks for posting your solution. Putting the FontAwesome font at the end works better for me, though; when it's at the front, all text is displayed using FontAwesome.