A better understanding of Adobe Experience Platform Data Collection: Tags

Tealium has a document called "order of operations" which explains internal prioritization of the load rules, extensions, tags, etc. I've not found the equivalent for "Tags" (or Launch). 

Generally, Tags’ rules are event-driven. You’ll notice that all of Tags’ rules must have events defined in them. E.g. when the user clicks something, the browser emits the “click” event, and any rule that has a “Click” evet from the Core extension will respond to that click. So there is not really an order of operations like what Tealium has. Instead, Tags’ rules listen to events.

Having said that, there is an “order of operations” that always happens when loading a page: LIbrary Loaded → DOM Ready → Page Bottom → WIndow Loaded. If you think about it, this follows exactly how browsers load a web page.

The real question I have at this point is, are there some things which get cleaned out of Custom Code sections (either in events or rules) during the library build process?  I've added lines and lines of code with console.log statements and such and it simply disappears from the library or never gets executed (ignored?) when testing on a site. 

No, Tags does not remove any custom code. What is most likely happening is that the rules that have these Custom Code actions are simply not being triggered at all.

However, Custom Code actions are always loaded via separate JS files, instead of being bundled in Tags’ JS library. As a result, if you’re running custom code when the user clicks a link, then it is possible that the user’s browser may not have loaded the custom code’s JS file in time before the browser had navigated to the next page. Thus your custom code action doesn’t run.

Last, what's the story with trigger() ?  Is there any limit to where and when it can be used ?

It is primarily used with a Custom Code event. There is an old, almost-10-years-old (!) article that describes how to use trigger() in a Custom Code event, with the example that you want a rule to run when the user clicks the middle mouse button: https://medium.com/adobetech/custom-code-event-type-6cde810ff09c