The TwentyFourteen add-on was created by another developer; he provides support here: http://wpdefault.com/forums/forum/styles-twentyfourteen/
For some settings not working, name the specific settings, provide screenshots if possible, and let @zgani know in his forum.
Before you do that, though, if the Customizer is only partially loaded, it may be caused by limited resources on your server. If errors are output, or the HTML doesn’t completely load all the way, it might be a sign that your server is running out of time or memory. These server settings may need to be increased in host-specific settings, .htaccess, php.ini, or just taken up with the hosting provider. Google PHP memory_limit, WordPress memory limit, and PHP time limit.
PS: In using a child theme, it’s pretty much all or nothing. If you see the Styles settings, then it’s set up correctly. If you don’t, try moving customize.json from the plugin folder into your theme folder. If you see some settings, or some settings work but not others, check to see if you’ve chanced the HTML structure in your child theme. Styles depends on the CSS selectors in a child still being the same.
