Question: what are some open ended questions to ask a girl?
Answer: How are you doing? (not for a superficial “good” but more of a what have you been up to)
What school do you go to?
Where do you work?
What do you like to do in your free time or for fun?
Do you have brothers and sisters? ... 
Do you want to go for coffee (or drink of choice)? ... 
Were you born and raised here?