how to add functions to my function.php using a child theme?

The site crashes, because you have a typo in that code. You’re missing an apostrophe at the beginning of the string:

// Custom Function to Include
function my_favicon_link() {
    echo <link rel="shortcut icon" type="image/x-icon" href="https://wordpress.stackexchange.com/favicon.ico" />' . "\n";
         ^ missing apostrophe
}
add_action( 'wp_head', 'my_favicon_link' );

Here’s the fixed version:

// Custom Function to Include
function my_favicon_link() {
    echo '<link rel="shortcut icon" type="image/x-icon" href="https://wordpress.stackexchange.com/favicon.ico" />' . "\n";
}
add_action( 'wp_head', 'my_favicon_link' );