Gifting an App Store app to an Apple ID that is part of a Family Sharing family?
If I gift the app to my friend, does the entire family get access? (This isn't a problem, but it's something that I think would need to be communicated, especially if others in the Family Sharing plan decide to use the app and then my friend later leaves the family)
  


Yes. After you gift the app to your friend's Apple ID, it appears as a purchased item under their account. If the app in question has family-sharing enabled, it would also become available to the other members of the family.


  
  If my friend decides to leave the Family Sharing plan, will she retain access to the app I gifted her under her own Apple ID, or will it revert to being owned by the Family Sharing family owner?
  


The app gets tied to your friends Apple ID. So she'd retain access. If the other family members have downloaded and installed the app before your friend leaves the family, they can continue using it. After your friend has left the family, the other members of the same family would lose access to download it for free.


  
  If my friend uses in-app purchase to buy an add-on for the app (not a transient item like coins or credits, but say unlocking a feature), will that attach to her own Apple ID (and thus be available should she disconnect from the family sharing plan) or will it belong to the family and thus not be available later?
  


The In-App purchases are tied to the Apple ID that purchases them, not the family. So she'd continue to have access to the In-App purchases made with her Apple ID, and the family she's a part of would not have access to it, irrespective of whether she remains a part of the family or not.

A very simple way to understand and get answer to these questions is this: There is no such concept as family ownership of content. Content such as an app purchase is owned by a single Apple ID, and it appears under the list of purchased item for the said Apple ID. If the developer of the app has enabled family-sharing for their app and someone from the family purchases the app, it becomes available for download to the other members of the family the Apple ID is a part of.

To understand more about Family Sharing, you can consider going through the following links:


Family Sharing - Apple
What types of content can I share with my family using purchase sharing?