Hey There,
Thanks for writing in!
1.) You are seeing PHP notices. You can get rid of this notices by disabling the debug mode. Please edit your wp-config.php file and set the debug to false.
define('WP_DEBUG', false);
2.) I could not replicate the overlapping logo and search bar issue. It could be a browser cache. Please clear the browser cache or use private browsing mode.
3.) The icons were not loading because it resulted to a CORS issue or Cross Origin Resource Sharing issue. Please decide whether you want www or not. You can change this settings in Settings > General and set the Site URL and WordPress Address URL with or without www.
Hope this helps.