1. is your rental include parking fee? If include, then even you don't have car, you have to pay. When I rented my previour apt., I got the same case, my parking lot was empty for almost one year, and I have to pay it with my rental.
2. Yes, like I said, in my old contact, they didn't specify which parking lot is mine, they just said they would give me when I get my car, maybe indoor, maybe outdoor. So CHECK YOUR CONTRACT!