Okay, you have a few of issues:
1. Don't create a
functions.php in your Child Theme, unless you actually intend to define custom functions.
2. If you do create a
functions.php, you cannot reuse function names from the Parent Theme, or else you'll get errors such as
Cannot redeclare header_style(). (This error is telling you that the function named
header_style() is already declared - i.e. is already defined somewhere else.)
3. If you create custom functions, always prefix the function names uniquely (usually, using the
theme-slug), in order to prevent function-name conflicts.
4. You may need to modify your Parent Theme, as it does not appear to be configured properly for Child Theming. For example, in
functions.php, this line is causing one of your problems:
require_once ( get_stylesheet_directory() . '/theme-options.php' );
get_stylesheet_directory() should instead be
The problem is that, when using a Child Theme, the Stylesheet directory refers to the Child Theme, and the Template directory refers to the Parent Theme - so what's happening here is that the Parent Theme's
functions.php file is telling WordPress to look in the Child Theme (i.e. the stylesheet directory) for the
theme-options.php file, instead of in the Parent Theme (i.e. the template directory), where it should be looking.