If I have an image field with multiple values, for example, how could I let users create edit and delete only their own images (i.e. that they upload and not anyone else)? I tried the field permissions module but it does not limit individual values of nodes.
I think your goal is to create a gallery which different people can upload their own images into it and then modify those images. Reaching this goal you can create a gallery content type with multiple images and a taxonomy or a referenced field so you can relate two galleries owned by two different people and in this case any user can modify, create or delete his/her own gallery. At the end you can create a global view for all images using Views module so all images posted by all users are listed inside and can be categorized using the reference field you have added.
If you want all images being uploaded to same content then you must use another approach which needs the ability of drupal module development, first of all you must create a new field type using drupal Field API. This field type must contain a image subfield and a user reference so you can have both image and its uploader in a same place. Then you can use hook_field_access to restrict access to field values in different operations.