How does it work if family shares a storage plan?

No. Each person has their own independent account, you are just sharing storage space. Nobody can see other people's files or iPhone content at all.

Think of it like sharing a warehouse, where each person has an independent section walled off, and only they have access to what's inside, but they are still all under one warehouse roof.

Note, you are not sharing nor altering the iPhone's local storage capacity. iCloud Storage is online on an Apple server and is used for Backups and Photos. It dos not increase your iPhones storage.

You can store documents and files in iCloud, but as it is a syncing service, there will always be a local copy of the file on your device. If you delete the local copy, it will delete the one in iCloud. ie. copying things to the iCloud Drive folder in the Files App, will not release any space.

For Photos, you can select the Optimize option in settings to reduce the file size and quality of the photos on your device while maintaining the original ones in iCloud.

If you need to make space, its best to offload files and content onto a computer.