Did they tell you why you need a new battery? That part does not make sense and it should have nothing to do with your symptoms. You should find a reputable Audi mechanic in your area that is not associated with the dealership. The advice you have been given in this forum is most probably the cause i.e, the MAF or fuel system problem (water or bad fuel pump). But your car is so new that niether of these should be the case. Have you contacted Audi of America regarding this?

AWOL