weird handling of double quotes when using cmd /c "echo" - cmd

Question

I'm trying to escape some calls in bat file and I found out that I don't understand even on simple example the weird handling of double quotes:
Try
cmd /c "echo " "%TEMP%" rem this gives: " "C:\Users\xyz\AppData\Local\Temp
cmd /c "echo" "%TEMP%" rem this gives: The filename, directory name, or volume label syntax is incorrect.
cmd /c "echo beg "TEMP" %TEMP%" rem this gives: beg "TEMP" C:\Users\xyz\AppData\Local\Temp
cmd /c "echo beg ^"TEMP^" %TEMP%" rem this gives: beg "TEMP" C:\Users\xyz\AppData\Local\Temp
cmd /c "echo beg \"TEMP\" %TEMP%" rem this gives: beg \"TEMP\" C:\Users\xyz\AppData\Local\Temp
Just open command prompt (cmd.exe) and paste code.
The results are the same when copy/paste to cmd.exe or running a bat file.
What I would expect is that cmd /c "echo beg \"TEMP\" %TEMP%" should work correcctly. At least according to http://daviddeley.com/autohotkey/parameters/parameters.htm#WIN .
But I don't understand output from all the samples. Anybody could explain me that behaviour?
Edit:
The site I'm referencing just explains how arguments are parsed on Windows. E.g. http://daviddeley.com/autohotkey/parameters/parameters.htm#WINCRULES
What is my expected output?
I just want to know how that passing of double quotes work.
Later I'd like to construct command lines like this one:
pwsh -noprofile -command "produceSomeStringsToFind | % { rg -g testfile* \" $_ some string that ends with quote\\\"" . }"
where rg is https://github.com/BurntSushi/ripgrep - where the \" $_ some string that ends with quote\\\"" part is regular expression where I need to escape the quotes.

Answer 1

From the help text of cmd /?:
[...]
If /C or /K is specified, then the remainder of the command line after
the switch is processed as a command line, where the following logic is
used to process quote (") characters:
1. If all of the following conditions are met, then quote characters
on the command line are preserved:
- no /S switch
- exactly two quote characters
- no special characters between the two quote characters,
where special is one of: &<>()#^|
- there are one or more whitespace characters between the
two quote characters
- the string between the two quote characters is the name
of an executable file.
2. Otherwise, old behavior is to see if the first character is
a quote character and if so, strip the leading character and
remove the last quote character on the command line, preserving
any text after the last quote character.
[...]
It becomes clear that you are facing the situation explained in section 2., because echo is not an executable file but an internal command. So if the first character is a ", it becomes removed and so becomes the last ", and all the other characters are preserved.
Now let us go through your command lines. So after being parsed and processed by cmd /c:
cmd /c "echo " "%TEMP%" becomes echo " "C:\Users\xyz\AppData\Local\Temp.
cmd /c "echo" "%TEMP%" becomes echo" "C:\Users\xyz\AppData\Local\Temp; then the command echo" is tried to be executed, but which is not a valid one, hence it fails.
cmd /c "echo beg "TEMP" %TEMP%" becomes echo beg "TEMP" C:\Users\xyz\AppData\Local\Temp.
cmd /c "echo beg ^"TEMP^" %TEMP%" becomes echo beg "TEMP" C:\Users\xyz\AppData\Local\Temp, because escaping with ^ happens even before cmd /c is executed, so it receives the already escaped literal " characters.
cmd /c "echo beg \"TEMP\" %TEMP%" becomes echo beg \"TEMP\" C:\Users\xyz\AppData\Local\Temp, because the \ is nothing special to cmd.
If you want to output the text "%TEMP%" (including the quotes), you could do this:
rem // This preserves all quotes, because the first character is not such:
cmd /c echo "%TEMP%"
rem // This removes the outer-most pair of quotes, because the first character is such:
cmd /c "echo "%TEMP%""
rem /* This removes the outer-most pair of quotes too, since `cmd /c` receives the already
rem escaped `"`; however, this could be useful to hide these quotes from the hosting
rem `cmd` instance, which avoids issues when `%TEMP%` contains special characters
rem (like `&` or `^`), which you would otherwise have to individually escape: */
cmd /c ^"echo "%TEMP%"^"