That's not 100% right, but close enough.
> 3. That's what I want to use, but PG changes \@some_array to \\some_array
PG changes the text of your PG file from \@some_array to \\@some_array, double backslash and at sign still present. Now it's an actual backslash character (as represented by \\) followed by the array. Which might be broken syntax or might be a string that is not what you intended, depending on the context.
> 2. Using \@some_array is the same as using [1,2,3]
There is a technical difference, although in most cases the effect is the same. \@some_array is a reference (think of that as an address in memory) to the actual array @some_array. But [ @some_array ] is a reference to a different nameless array that has the same entries in it. And [1,2,3] is similarly a reference to an anonymous array.
So far, everything mentioned is just perl syntax. A PG-specific tutorial on perl would be nice, but it's hard to put in the work for that given there is a lot about perl in general on the internet.
Then the one thing that is specific to PG is translations. These are how PG modifies your problem file text before it actually gets processed. The two translations that matter here are \ to \\ and ~~ to \. I believe these are the only "gotcha" translations. They are happening at the bottom here:
https://github.com/openwebwork/pg/blob/d17c2beddf44d1bdcfabe7c1f6dff8f561dee752/lib/WeBWorK/PG/Translator.pm#L1334
Higher up in that list, you can see things like how "BEGIN_PGML" is translated into an actual perl construction for a multiline text string. Those translations are less mysterious.
The tilde issue is mentioned here:
https://webwork.maa.org/wiki/LaTeX_Tips_And_Traps
But that page is actually mostly information about writing PG in the era before PGML. Other things on that page do not apply if you are using PGML. If there were a fundamentals page about coding PG, it should have this thing about backslashes and tildes in it. Although, it's hard to talk about until the perl basics are understood first.
In wiki resources you were using, does any place seem natural to add an explanation about blackslashes and tildes? We could try to make edits there.