You sohuld be able to do this with Graph API. In order to use it you probably would need to register a facebook app first and then request some extended permissions from your users through authentication process to be able to access their private data.
To get tags for a specific photo you would use the following graph api path:
https://graph.facebook.com/<photo_id>?access_token=...
It should return a JSON object that contains tags
array with a list of users tagged in this picture, as described here. To access photos from a user you probably would need to request user_photos
extended permissions (unless it is you or your friend).
To get photos the user has been tagged in, you can use this graph url:
https://graph.facebook.com/<user_id>/photos?access_token=...
You would need user_photo_video_tags
and user_photos
permission for that, as described here.
I don't know anything about .NET side of things, sorry.
I know this all is a bit overwhelming to grasp right away :) I think you need to read through the docs first, register an app, find .NET API library and try to make an authorization process. After that Graph API is pretty easy to understand.