Can I (we) add an old Apple I.D. to Family Sharing to access purchases?

As the organizer, you can share whatever purchases were made on the AppleID you used to set up Family sharing and are logged into the Music and App stores with. If you change that AppleID, then you lose access to the things purchased on that, as you’d now be setting up effectively a new family share with that other AppleID. The organizer can only have one AppleID in use with a given family share setup at any one time. Every time the organizer changes AppleID, it’s a new family share.

No. Purchased content cannot be transferred across AppleIDs. If you sign out the current AppleID you will not be able to update or reinstall any of the purchases made on it. You’d have to switch AppleIDs every time there is an app update, or somebody needs to reinstall the apps. And you can only change the AppleID associated with the Music and App Stores once every 90 days.