where does permissions requests go?

I'm not using family sharing, but if you are the family organiser then you you should get a notification about the purchase which you need to buy or deny the purchase : Request and make purchases with Ask to Buy - Apple Support

If you're the organizer, you can use these steps to make or decline the purchase from your iOS device with iOS 8 or Mac with OS X Yosemite:

1. Open the notification to see the item that your family member wants to get. (See your notifications on your Mac or iOS device.)
2. Approve or decline the purchase.
3. If you approve, you need to sign in with your Apple ID and password to make the purchase.

After it's purchased, the item is added to the family member’s account and shared with the rest of the family group. If a family member downloads a previous purchase again, downloads a shared purchase, installs an update, or uses a redemption code in the store, the organizer won't get a notification.

If the organizer doesn't make the purchase or decline the request, it will be deleted after 24 hours, and the child will need to make the request again.

Hi, this question wasn't actually answered. The problem that many people have is that sometimes the authorization fails, and the notification just disappears from the list of notifications. This is really stupid and frustrating, especially when I'm 10 hours ahead of the person requesting the app and I basically have to wait 24 hours to get the notification. Sometimes it takes me a week to authorize one stupid app request.

Please fix this, or at least answer the question that was asked?

Please fix this

You already know that you are talking to fellow users (I therefore don't work for Apple and can 'fix this'), that these are user-to-user forums, and that Apple are not here.

least answer the question that was asked?

I answered OP's question (he/she didn't reply saying that I hadn't), if you have a different question start your own thread.