Need help creating child theme for Arcade Basic

The changes I had made in the theme’s customizer did not appear though, I had to go in there and redo those. I am assuming that is because I did not create a customizer.php file in the child theme??

No, it’s because any changes made in the Customizer only apply to that particular theme, and since WordPress considers a child theme to be a separate theme from the parent theme, the customizations won’t apply to it. This is the same reason why you’ll likely have to reassign any navigation menus and sidebar widgets when you switch to a child theme.

If I understand correctly, all changes I will be making to these files I will be entered into the child theme’s function.php file, correct? But before I do that, I need to create files in the child theme for each of the files I am editing and on top of that, in the functions.php file I need to enqueue them, correct?

No, you only need to enqueue stylesheets in functions.php. So you will need to enqueue editor-style.css by using add_editor_style(), but if you want to make changes to the PHP files, you simply need to copy them into your child theme’s folder and edit that copy. WordPress will use the PHP files in your child theme first and use the parent theme’s PHP files only as a last resort.

I would also like to create files for individual page changes as well so I can make changes to any particular page instead of site wide. How would I go about doing that?

You could make separate page templates, or you could use some custom CSS, depending on what you’re trying to do. If you need more help with that, it’s best to make a separate topic and post a link to your site, as well.

You can use the code I provided to properly enqueue your editor stylesheet:

function my_theme_add_editor_styles() {
    add_editor_style( 'editor-style.css' );
}
add_action( 'after_setup_theme', 'my_theme_add_editor_styles' );

That snippet of code should be added to the end of your child theme’s functions.php, right after this snippet (from your original post):

<?php

add_action( 'wp_enqueue_scripts', 'theme_enqueue_styles' );
function theme_enqueue_styles() {
wp_enqueue_style( 'parent-style', get_template_directory_uri() . '/style.css' );
wp_enqueue_style( 'child-style', get_stylesheet_uri(), array( 'parent-style' ) );
}

The TinyMCE editor is the html editor on in the wordpress admin correct?

Yes.

And this is basically to add extra features to use in the there only, nothing to do with the front end of my website

Not really, no. All this does is change how the HTML editor looks. If you’d like to add features to the HTML editor, you should try a plugin instead: https://wordpress.org/plugins/tinymce-advanced/