You have restrictions placed on your device by the Organizer of the family plan. That is why you don't see the App Store and unable to delete apps. You don't need the App Store to delete apps, those are 2 different restrictions that are placed on your device. One to prevent installing apps where the App Store is removed, and the other to prevent deleting apps where the only option is to remove from Home Screen.
If photos are synced from a computer, they cannot be deleted from the iPhone. You would need to connect the iPhone to that computer and remove the photos from the sync option and resync again without those photos selected. Not sure if that is what you are experiencing, but it is one reason why they cannot be deleted.
And finally, if this is the iPad Air 2, the latest version of iPad OS is 15.8.5 and cannot be updated any further.