How to store / access files in child theme folder

Can you place custom .php files directly inside the child theme
folder?

Yes, of course you can. WordPress is PHP. What works in PHP works in WordPress.

Some of the research we found says you must write your custom PHP
functions inside of the functions.php file.

Nonsense. Many themes segregate code into multiple files, including “Twenty Fifteen”. This is not only OK but is usually wise as it helps keep your code base organized and manageable.

If we are forced to write all functions inside the functions.php file,
how do you “call” a function within a function? Using “includes”
doesn’t make much sense if all of the functions are inside one file.

This doesn’t make sense. User function definitions in PHP are all global. Once loaded, they can be used anywhere. That is basic PHP (which works like normal in “WordPress”). There should be no issue with “calling” a function within a function. If the function has been defined, just use it.

If you CAN STORE the custom .php files inside of the child theme
folder (as separate files and file names), do you call them with an
“include” like you would in regular HTML/PHP site files (not inside of
WordPress)?

You can, and yes. require, require_once, include, and include_once work in WordPress like normal. WordPress is a PHP application. PHP works in WordPress. I honestly don’t understand why so many people seem to think that it doesn’t… that WordPress somehow breaks PHP.

Where in the child theme do you store Javascript files?

Wherever you want. Usually a folder named something like “js” or “javascript”, but that is up to you. You could store it in a folder named “fred” if you want or in no folder at all.