Docker images and network storage are not related to each other at all, so I don't know what you are actually asking here. They are 2 completely different and separate things.
but you can move your files from your image's pod container to the network volume storage by copying or moving it to /workspace if you have your network storage attached
What local one? container disk? edit pod and increase the container disk, but I suggest storing things on persistent storage and not container storage.