Hi Christian
Let me make a few observations about child themes before turning to some specifics. (The best starting point for reading about child themes is the official Theme Developers Handbook: https://developer.wordpress.org/themes/advanced-topics/child-themes/.)
A theme will have a functions.php file, and you can add one for the child theme, too. Unlike template files, where the files in the child theme if present replace those in the parent theme, both the child and parent functions.php files run (in that order).
You cannot declare the same function twice in PHP, and functions added to the parent functions.php are ideally 'pluggable', meaning that they test to see if the function already exists before declaring it.
That way, the child theme can declare the functions and these will be used instead of the same functions in the parent theme functions.php.
Functions in the child theme don't need to be pluggable, you can just go ahead and declare them. (You have copied the pluggable wrapper when reproducing functions from the parent in the child.)
Your child theme uses the function ref_enqueue_main_stylesheet to enqueue the main stylesheets. You have commented out style.css for the parent theme. That includes a lot of default base styles which are no longer available to your site. That may be intended, just be aware of it.
You then replace ref_register_scripts from the parent in your child theme.
Everything you have done there looks fine to me.
For theme_js, I believe you should be able to remove it (it is used by the example Reference Sites). Try removing it and only add it back in if you discover some expected functionality not working.
The comment-reply script is only needed if you want threaded comments on your posts, if not it is superfluous. (Note, though that it would never be loaded if you do not allow comments, as there is a test for this before the file is enqueued.)
Lastly, there should not be any problems switching out the Bootstrap CSS file for minor version variants.