You opened with a question that only takes information from her without getting anything in return. She would only be motivated to answer this question if she was very interested in you before the conversation began.
She ended up answering your opener question, but her answer was straight-forward and dispassionate. I'd guess she just answered you to be nice and hoped the conversation could be salvaged.
The questions you asked aren't bad on their own, they just shouldn't be used to get a conversation started.