The Amrikiya has to go first?
The adjective that is closest to the noun it modifies in the English sentence remains closest to the noun it modifies in the Arabic sentence.
If you want it marked correct, it seems yes, but why?
Slightly different meanings: A syrian american girl = a girl of a syrian family who lives in America, while an american syrian girl = a syrian girl who comes from America
Yes yes yes i got it right
Is this flip flop of Syrian and American also valid while writing the same sentence for male gender?
Why American come first ?
See Ronald Lett's answer.