The icons are not displayed because there is an issue with your web hosting setup.
Your site URL is travelstryservices.com but the URL that is serving your site and all it’s files is 66.147.244.175/~ravelst6/.
Because they are not the same, it will prevent the icon font from loading. This is also stopping the javascript files needed for the header area and the mobile menu, which is why the header image area is not working correctly.
You will need to contact your web hosting company and ask them to correct this issue.