I echoed out this $google_map_api_key = get_option('talimi_mapapi'); and its working fine.
try in functions.php add require_once get_template_directory() . '/page-templates/theme-settings.php';
or add wp-load.php in your file.
if you are using multi-site then try <?php get_site_option( $option, $default , $use_cache ) ?> reference https://codex.wordpress.org/Function_Reference/get_site_option