You should store the blackberries in a low-humidity, low-moisture part of your fridge, such as the middle rack.

They are suitable for freezing but to avoid them clumping together you should flash freeze them first. Wash and dry thoroughly then place on a baking sheet and place in the freezer for about 3 hours.  Then take them out and transfer to another airtight container where they should keep for up to 6 months