Yes, in the garage next to the Omni hotel there is paid parking. I think it is called red parking. Parking can be validated at the restaurants with a purchase .
Delta lot is close to the store. But I am not sure you can purchase anything during game days. On off days where there isn't a game, the store is open to the public from the Battery. During game days you can access the store from inside the park.
Yes you can park in the lot around the red deck or delta lot and the one across the street
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