Question: Why "A co" is used and not "Dlaczego" or "czemu"?
Hm, it could be tricky for a Polish learner ;).
'A co' is the colloquial form used in informal conversations, for example when two teens talking to each other.
Dlaczego / czemu could also be used, BUT to make it sound correct you'd have to add the word 'pytasz' (
asking) after these. So:
Dlaczego
pytasz, szukasz partnera?
Czemu
pytasz, szukasz partnera?
So the bottom line is, 'A co' is informal of 'dlaczego / czemu
pytasz' and it should not be used in a formal setting.
"Jestem wolna" in Polish means (literally): I'm available. 'Wolna' = 'available' in this context.
You're right that 'wolna' also means 'free' but in this case the conversation is about dating, not freedom; hence, the translation is 'wolna = available (for dating/meeting, etc.).