IOS – Who owns the Family Sharing purchases

Before Family Sharing, you could take someone else's iOS device and sign in to the app store with your account and download all/any apps you choose.

At that point, your password was needed to update, but signing out didn't delete the apps or in any other way prevent them from working. Let's set aside in-app purchases for the time being.

Family sharing changes this in that when someone joins the "family" - their Apple ID is used to download and update other family member apps. They do not show up in your purchases, they show up as the other named family member's purchase. All that changes is the password needed to install and update.

When you as a family member remove yourself from the plan - you get a warning that lists what will happen and basically, you immediately lose access to the purchases, photos, calendars and other items that were shared in the plan.

Rejoining the family would then let you re-download and re-sync the items.

You'll probably want to find a better way to use the family service than routinely joining and leaving or skip the family share and use the older method of signing in to multiple devices which doesn't immediately remove/revoke the items.

Yes. This is possible. The instructions for all the necessary steps can be found here, provided you have OS X 10.10 Yosemite or higher. When someone in your family requests to make a purchase, you will get a notification on your Mac. (You can find past notifications in the Notification Center). You can approve the request directly from the notification, and it will ask you to authenticate with your Apple ID credentials.