As you say 'used to' implies, whereas 'in old the old times' fleshes it out. Hemingway liked it as short as possible and used to deride Faulkner for his redundant, elliptic and what not sentences. Both won a Nobel Prize. For literature. Just saying. It is a matter of style when you write your own text.
But ... when you have to translate a text you better keep it as close to the original as you can, which in this case contains 'eskiden'. So 'in the old times' is not redundant in this case, imho.
Sometimes, in language teaching/learning, it is necessary to do a literal translation; it helps the learner know how the target/foreign language works in terms of sentence structure and grammar. That is why I strongly suggest that two translations be offered in these exercises (since the translation method is the one being adopted by Duolingo): the first is the proper translation that makes sense in the language in which the sentence is written (here English) and the second is literal translation exclusively for learning purposes. That's what I do in my classes and that's what I would do if I had a program like Duolingo.
I once used to love you was labelled incorrect - should have been I formerly used to love you. No English speaking person would use the word formerly in this context, and one meaning of eskiden is once.
On a second attempt, I formerly used to love you was labelled wrong - it should have been formerly I used to love you.
Actually, "I used to love you before" makes sense in contexts where "before" refers to some understood event/action...
For example: She: "you really changed since my last trip alone...", He: "Yeah, I used to love you before..." Another way to think it is as:
- "I used to run" being equivalent to "I was running" (or past continuous)
- "I used to run before..." being equivalent to "I had been running before..." (or past perfect continuous). Where before has contextual meaning.
While I am not sure whether this meaning works in Turkish, it does apply to other Indo-European languages.