"My family really likes eating Northern food."
我家人很喜欢吃北方菜 (with no 的 at all) is accepted, but I just put "我家人很喜欢吃北方的菜" and it was rejected. I don't think 北方菜 is such a set term that inserting 的 would make it wrong. (reported 29.1.18)
I agree. In another exercise 的 was not used between family members.
I think you're referring to 我的家人都... Which is literally "My family ALL..." Because "all" isn't in the English here, I wouldn't put it in the Mandarin. However, that is a common phrasing, emphasizing that everyone has the same opinion.