I guess we’ll never know.
Is "så" an abbreviation for "sådan"? Could "sådan" be used instead, and would it change the meaning of the question?
No, så is a word of its own. English can use "such" in basically the same sense as "so" here, but Swedish sådana doesn't quite work as a substitute. You'd be understood but people would think it sounds quaint, or off.
Why is “why does she have so long arms?” wrong?
That's definitely correct. I'm adding that now.