Overriding methods in a child theme

I would like to refer back to this answer on one of your previous questions about this subject. As said in that answer, you should never make changes to the twenty thirteen theme, and for that matter, to any theme/plugin you are not the author of, this includes core files as well.

But I don’t quite understand, how to put the 2 above changes in the functions.php suggested by the doc?

OK, you have your child theme set up, now you need to create a file in your child theme’s root and call it functions.php. Open this file and add an opening php tag (<?php) right at the top and press enter and save this file

For the first line of code, you can simply just change the custom-header arguments with this function

function my_custom_header_setup() {
    $args = array( 'height' => 800 );
    add_theme_support( 'custom-header', $args );
}
add_action( 'after_setup_theme', 'my_custom_header_setup' );

This will go into your child theme’s functions.php starting on line 2

For the second part, simply copy the twenty thirteen’s header.php file to your child theme’s root, open it up, make your changes and save it. Your child theme will now use this header.php instead of twentythirteen’s header.php. You can use this method for all other template files, except functions.php and functions.php related files, as you will trigger a fatal error. For example, if you need to make changes to index.php, simply copy it to your child theme, open it up, make your changes and save the file. Your child theme will then use this index.php, and not that of the parent