Well , actually the error is pretty minor , on your callbacks you have wrote
function logo_field_callback(){
$option = get_option('thanathos_social_logo_options');
echo '<input type="text" id="logo" name="thanathos_social_logo_options[logo_field]" value="' . $options['logo_field'] . '" />';
}
function facebook_field_callback(){
$option = get_option('thanathos_social_logo_options');
echo '<input type="text" id="facebook" name="thanathos_social_logo_options[facebook_field]" value="' . $options['facebook_field'] . '" />';
}
as you can see, you load as $option but print as $options, that is your only issue