Using family sharing- When requesting to purchase an app, the icon saying “A request has been sent to the family advisor or you can approve in person in this device” shows up but the link regarding approving in person does not work and has not worked

When it says "approving in person on this device" they are talking about the Family Organizer, (or parent) approving.

In other words, you can tap "approve it in person" if the organizer is nearby and then they enter their user name and password on your device to approve the purchase.

iTunes [Store] Support - Use this form for assistance with account and billing, code redemption, or purchase questions - https://ssl.apple.com/emea/support/itunes/contact.html