Can we share all photos in a single, common photo album with Family Sharing?

Not all photos but up to 5000. The following is from this Apple document: How to share albums in Photos on your iPhone, iPad, and Mac - Apple Support

Shared Album storage limits

A shared album can hold up to 5000 photos and videos.

No.

You can only share via shared albums. See the following from Family Sharing - Apple

When you set up your family, a shared album is created automatically in the Photos app on all family members’ devices. Everyone can add photos, videos, and comments to the album whenever they like and get notified when something new is added.

Even if you have a shared iCloud Storage plan, all photos are not shared. See the following from Share an iCloud storage plan with your family - Apple Support

When you share a storage plan, your photos and documents stay private and everyone keeps using their own accounts with iCloud—just like when you have your own storage plan. You simply share the space available in the iCloud storage plan with your family members, so you only have one plan to manage.

You may want to let Apple know if it is an option that you want: https://www.apple.com/feedback/icloud.html