What access do I have to grant for anyone to do deep customization of the theme?
Will a cPanel access do the trick?

Or anything similar, that may give this option to filter a filter.
Select what categories to be shown on the site.

Thank you!
It worked out :o)
Problem solved!!!

I go to Appearance > Themes
I find my child of Enfold, the Enfold template and some other templates.
Option on child is ‘Customize’ and on Enfold ‘Activate’ and ‘Live Preview’.

May I lack some options because of the license type I started with?
I now bought a new license, but started with a split license…

At Edit choose there is stated:

/*
Theme Name: Enfold
Description: A superflexible and responsive Business Theme by Kriesi – <br/> Update notifications available on twitter and facebook:<br/> Follow me on twitter<br/> – Join the Facebook Group
Version: 3.2
Author: Kriesi
Author URI: http://kriesi.at
License: Themeforest Split Licence
License URI: –
Theme URI: kriesi.at/themes/enfold/
*/

/*
* PLEASE DO NOT EDIT THIS FILE!
*
* This file is only in your themefolder for WordPress to recognize basic theme data like name and version
* CSS Rules in this file will not be used by the theme.
* Instead use the custom.css file that is located in your themes /css/ folder to add your styles.
* You can copy a style rule from any of your css files and paste it in custom.css and
* it will override the original style. If you just want to add small css snippets you might also
* want to consider to add it to the designated CSS option field in your themes backend at: Theme Options->Styling
*/