It should definitely be "the dog's tail" in English. Saying "the tail of the dog" would sound awkward at best to a native speaker, although it's understandably confusing because sometimes we do prefer "of" (the periphrastic possessive).
That's a very good question. It's a general thing for all courses and not specific for our course, so it should be discussed in the general forums, and it is. Here's a link to one of the most recent posts about it: https://www.duolingo.com/comment/14171868