Is the order of constituents relevant in this sentence? or is it correct to say "לא ישתנה שום דבר" too?
It's completely correct, although a bit less natural.
Can I say שום דבר ישתנה? I feel that it's the same..
Hebrew uses the double negative. Think of "שום דבר" as "even a thing" (not sure if that's the literal translation), so the "לא" is needed to make it "not even a thing" (nothing).
Shum davar lo yishtane
I don't know who you are but I'm grateful for your pronunciations, when Duolingo doesn't provide it in their examples ❤. Be blessed