Why not 'unhappy' for 'nešťastných'?
Translations using "unhappy" are accepted.
Could the reflexive word se be closer to snažit without changing the meaning of the sentence? It's feels incredibly odd, not only by the distance but also due to the verb přestala in between
Se follows the second position rule.
Any reason why unlucky isn't accepted?
It is accepted, we need the complete sentence.
Is it acceptable to put Zofie at the beginning of the sentence (in English)?
Yes, it is.