Hi ginkku,
thanks for using MH Edition lite.
1) How do I enable custom post type support on MH Posts List widget? I’m using a child theme.
You would need to code your own version of the widget within your custom child theme and then modify the query to include your custom post type: https://codex.www.ads-software.com/Class_Reference/WP_Query#Type_Parameters
Or you could make use of a plugin which provides particular widgets for custom post types.
2) How do I change the default placeholder featured image directory to my child theme’s /images directory?
You have three options to achieve what you have in mind:
1.) Simply replace the image placeholders within the /images folder of the parent theme.
2.) Modify all parts of the theme that use image placeholders within your child theme to load the placeholders from the child theme directory: https://codex.www.ads-software.com/Function_Reference/get_stylesheet_directory_uri
3.) Instead of replacing the image placeholders, you could also just hide them with some CSS: How to hide gray image placeholders in your theme.