Has there been a time previously when this plugin was working on your WordPress server? Or has it only ever resulted in this error?
The error message about failing to send a request to the Font Awesome API server indicates a problem on your WordPress server, and possibly some kind of firewall rule or other network configuration that is causing your WordPress server not to be permitted to contact the Font Awesome API server to retrieve the metadata it needs.
This happens sometimes when web hosting providers have unnecessarily restrictive rules in place and can usually be easily resolved by relaxing the appropriate policy on the server.
This other issue is an example of the kind of problem you might be facing.
If your WordPress server’s networking rules are configured appropriately, you or your web hosting provider should be able to run this on the WordPress server:
curl -H "Content-Type: application/json" --data '{ "query": "{ release(version: \"latest\") { version } }" }' https://api.fontawesome.com
And see a response like this:
{"data":{"release":{"version":"5.12.1"}}}
(but with a more recent version number)