Yes when storing berries in the fridge it's best to cover the berries while in the fridge.
When you store berries don't bunch the berries all up together as when you do bunch the berries all up together without air space between them they will not be able to breathe which causes them to spoil quickly.
When storing berries in the fridge it's best to store the berries in the same container that you bought the berries in from the store.
The berries should last between 3 to 4 days in the fridge but you should eat the berries as soon as possible.
If you notice a few berries getting moldy then remove those moldy berries right away to protect the other berries and eat those good berries up before they have a chance to mold themselves.