Snippet inside ArticlesAnywhere doesn't show

It is probably due to the system plugin ordering. Try changing the ordering of the plugins in question.
See: regularlabs.com/blog/242-plugin-order-is-important

Not sure what you mean with the 'Joomla Fields content'...
Do you have this online so I can take a look?

And do the things that you are missing show when you place the {articles} tag in a normal article (without other stuff around it)?

If you can reproduce this on an online environment to which I can get access, I am happy to look into this.

Ok, so this concerns the Joomla core field plugin. I thought you meant the field datatags of Articles Anywhere.

The core plugin is a content plugin, which has limitations. Especially when using combinations of plugins like you do, the core content plugins just don't get a chance to see the final content that contains the tags.

But seeing you are using Articles Anywhere anyway, why not use Articles Anywhere for these fields?
The syntax is much clearer anyway, as you can use the actual field names, instead of their IDs.

Just surround the whole article in {article}...{/article}
And replace {field 285} with [285-course-description] (and all the others).
I am not sure why you are repeating the IDs in the titles and names of the fields, but that's down to how you want it set up.

By the looks of it, the whole article (ID 379) is just a template that shows a bunch of fields. No real content in the editor itself.
So why not place the whole thing in a snippet, and output the fields through Articles Anywhere as mentioned above?

Yup.

Yes, you can do a LOT with Articles Anywhere! ?

You are using quotes inside the title. This messes up the syntax.Tabs & Accordions would see the title as being:
So instead do:

Can you eliminate the Accordions from the mix?
In other words: do the fields show when you place the Articles Anywhere code outside the accordion?