I've made things much simpler.
I've created completely new joomla page -> fresh install of joomla 3.8.6 + fresh install of zentools2 2.4.0
I've created 1 new zentools2 module to display grid with introtext articles.
It is not possible to create custom css for module. First there is a message that "Custom file created for this module.", but in fact it was not. After save we have: "Custom file not yet created.
Click the Create custom css button below to create a css file that can be used to specifically target this module."
I've updated site information, please feel free to do whatever you need to test it.
I'll be grateful for your help, because I don't know what am I doing wrong. (Or maybe it's a bug?)