For some reason I'm getting pinged about this today and realize that I've never been notified about Reported Profile Pictures. When I went looking I had well over 1,000 Reported and 49,000 Submitted. So, first, there are no notifications I'm aware of that related to Profile Pictures.
It seems like most reports are accidental clicks on people's pictures, so I wanted to bulk approve them, but there's no API for this that I can see. There is no API for managing avatars at the account level, aside from at the individual user level. Also, there appear to be individual user permissions for the "lock" feature, but again no API to update them. That's really surprising.
You can edit an individual user to set an avatar url, and you can get the unique token, but nothing I can find in the API documentation indicates a way to manage reported or submitted pictures.
There are two "hacks" I used to at least work on the Reported profiles.
1. The url supports a per_page parameter, e.g. /accounts/1/avatars?avatar_state=reported&per_page=100 will display 100 users in the UI.
You could change this to batch lock or delete too.