Can I use custom fields inside custom fields in Drupal 7?
Please let me know if I'm misinterpreting your question — essentially, you're asking how to group up fields of content that appear frequently together on your Drupal site? Without using Field Collection... hmmm...

Well, first potential option is the Field Group module. However, it may not be exactly what you want seeing as how you mentioned Field Collection. It may be worth looking into though. Not sure it supports translation though.

The next potential option I see is changing the actual Image entity through the File Type interface provided by the Media module. At this screen, you can actually adjust the Image entity to contain extra fields. In doing this, all you would need then is place the Image field in your content type. The user uploading an image via this Media field would then be prompted to add the linked headline and a brief description after uploading the image.

Because the Media module documentation does an AWESOME job of explaining how to modify an Image entity, here is the documentation page about managing/editing file types — scroll down to the start of the section "Manage the Display of Images (Manage File Types)". After adding these fields to your Image entity (or a new entity), you'll be able to manage the display like you would for a content type.