"This cafe is very good."
I agree with you on the first sentence. However, if I were in Japan, I would definitely use ここの because it makes more sense to treat the cafe as a location rather than an object. But in English, I prefer to say "This cafe" because it avoids redundancy in the English language. Duolinguo suffers from this problem, and I have mixed feelings about whether Duolinguo should be consistent or accurate. And I have a feeling the staff at Duolinguo may also have these mixed feelings.
Even in English, using "terribly" in this same manner isn't really used in casual, daily speech by us mere peasants, it sounds snobby, and I feel inclined to suddenly acquire a posh, upper-class accent saying it, haha.
"This meal is terribly delicious". "I agree, this food is awfully delightful, care for a brandy after, old chap?" "Oh, rather!".... Yep, it feels like I've accidentally stumbled into Eton College, or maybe the tv show Downton Abbey.