This thread is resolved. Here is a description of the problem and solution.
Problem: My images are landscape photos and therefore not language specific. I would like to translate captions and image names only. In this context, which settings should I use both for existing content and new content? Solution: I think that having all the options from Dashboard → WPML → Settings → Media Translation checked is the best option. You won't be able if you'll use them this way.
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