I am not sure how important it is for you to learn how the wiki text is translated to HTML, more that "what WikiText results in what output?" Please clarify!
One thing to keep in mind is exploring your TiddlyWiki's own internal workings is a great way to learn and discover. In part due to TiddlyWiki's Open source status and in part because it is designed to allow its user interface and working to be freely modified you can actually be on a desert island with no internet and teach yourself about tiddlywiki. Of course this can sometimes be time consuming when some good documentation would help.
The challenge for a new user, like for any system, is getting and understanding the keywords that describe something. For example the "magic tags" you mention, are most likely system tags thus if you look here
https://tiddlywiki.com/#SystemTags you will see a short explanation for each, many of these will also be the magic tiddlers you speak of.
Learning about the page, view and edit templates and how they work is also useful, because then you can track how something appears in front of you.
The way the toolbars and buttons work is also a key area to learn, because it enables so much, including customising or making your own buttons.
I am now reworking my "TWInternals" Tiddler to remove a dependency on a plugin and I will let you know here where to find it. This tiddler basically lets you peek into a range of internal tiddlers and settings, and can act both as a reference and a step by step exploration to learn more.
Regards
Tony