Overriding File Entity fields when attached to a Node
There's no easy way to do this for files or images, which are essentially reference fields. There's no native way to do this for any type of reference field in Drupal. For example, you can create a reference field to a node, but override what the node's title is in a certain article when you reference it.

Typically what people recommend is using a Field Collection or a Multifield that consists of an image field + whatever field you want to have as the 'use this value only when this image is used here' stuff.

For captions, I know we added a caption filter specifically in Drupal 8 core, but I cannot find if it got back-ported for Drupal 7. That would be handy to have and use now.