Say John, Jane and Mark are all tagged in a photo - if they consent by installing my FB app, can I then display that photo on a site outside of FB (regardless of their privacy settings)
What you are looking for is a deeper probe into the facebook graph API to find someone's photos and their tags. It's likely to get hairy.
I'd recommend getting started at https://developers.facebook.com/docs/reference/api/ You will probably need to use FQL.
One thing to note is you are now facing a double the adoption issue. Instead of just getting one person to start using your app, you are now reliant on two people to do so.
A simple way to get some profile pics on your site is https://developers.facebook.com/docs/reference/plugins/facep...