Hello,
1) Please Go to Appearance >> Customize >> Site Identity and try changing the Site icon. Then clear cache and check back.
You can read the following article for help:
https://www.wpbeginner.com/wp-tutorials/how-to-add-a-favicon-to-your-wordpress-blog/
And if you have any issues then please check how it works with the default wordpress theme just to check whether the issue is with our theme or not.
Because the default Settings for the Site icons are controlled by WordPress itself and our theme doesn’t influence.
2) You can find all the icons from the following link:
https://fontawesome.com/v5/cheatsheet
Best Regards