It may not be feasible to acquire PUZ files directly from the New York Times as they ended their PUZ archive in August 2021.

I think creating a Themeless Stacks won't be easy, but it would be great if this feature is established.

If you haven't experienced this issue before, it's possible that it's a rare occurrence or specific to the particular puzzle you were working on. One potential explanation could be a mismatch between the words accepted by the software and the words listed in the "Words Used" section.
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Yes, there are resources available for crossword constructors to check if their theme idea has already been used. One such resource is "XWord Info" (xwordinfo.com), which provides a comprehensive database of New York Times crossword puzzles, including information about themes, grid entries, and clues. You can search for specific words or themes to see if they have been previously used in NYT puzzles. Skilled drywall contractors in Fort Worth

I'll try to help...

I don't understand the concept of ordering these dictionaries in the Preferences list. Why position one above or below another if they're all going to be used together in a single list (are they)?

On this concept of ordering dictionaries, think if you do something that's a special topic.  You might compile a list of baseball players and teams and stuff for doing baseball theme puzzles, and want that stuff to appear first.  Basically "use this, but if you can't use this, then use the next one".

Why keep the MyEdits.dict dictionary above the others (or not)?

The thought there is that you're going to prefer the words you added yourself over something general.

Do I need to merge dictionaries? What exactly happens when you merge dictionaries?

The basic idea here is that you'll have lists of words in disparate places which will be a lot slower to process.  So if you merge them, you can get one file with words that aren't duplicated and therefore is going to process better.  For myself, I collect/create word lists (about 35 MB right now) via my own processes.  (Frankly that's been more interesting to me than doing grids since I can code and have created processes like pulling data out of PUZ files.)  But I try to merge the generic word lists every once in a while too so I can have a universal file I can throw out.  I need a good way to knock down the OED words, basically the stuff people see as "junk fill" these days. (Though the OED list has been great for me trying to pattern match old grids.)

Why would I need to use the Edit-->Save Dictionary command? Which Dictionary does it save, how do I choose this (DO I even get to choose this?)?

I don't know much about Crossfire and this function, but the idea is to give you the ability to be able to add words and save them.

What are the ramifications of having multiple word lists wrapped into one (does this even happen?) when some are scored using 0-50 scale, others use 0-100, and some don't score at all? Should I merge these together? Won't that Frankenstein words of different scoring scales into each other and kinda render the whole point of using these scores moot, since it will all be unstandardized?

I think it orders preference based on the numbers, which will generate an issue if different word lists have different scoring ranges.  I don't score my word lists when I generate them, but the idea is that you assign the score to each of the words based on your preferences.  I haven't gotten into Crossword Compiler that much, but I'd prefer to see a list of possibilities and then actively select the word as opposed to auto-filling.

While completing fill, if I add words to a grid on the fly that aren't in "my dictionary", do these words automatically go into my dictionary or must I add them/save them? But what does "my dictionary" even mean, when I have multiple dictionary files to choose from?

I think you have to explicitly add them and save them.

What about if I want to eliminate all the scores from all the entries, must I do this one word at a time? In each different dictionary? Or can I do one big sweep and zero (or 100) them all out in one fell swoop? How do I know what score to give words that aren't scored, if I want to do so?

I don't know if there's a function in Crossfire that will remove all scores, but you can either strip them out via code or by knowledgeable use of a spreadsheet program.  I think in the raw version it's just CSV text, so you can just rename the extension to that and then load it into the spreadsheet program and delete the scores and save.  Or edit them if you want.  If you want to score words, you just give it a number based on your personal preference for seeing the word come up in your grid.

how do I properly set up and start using my dictionary(-ies?) and word lists from the ground up? How is a Dictionary different from a Word List (is it?)?

Go through the file and see what kind of words you like and don't like, score them appropriately according to your preferences, and go on.

Anyway, hope that helps some.