It would sound extremely strange, "at" being used to describe static position. We can say "She's at the park" to say where she is, but running involves movement around a space or area, in which case we use "in". I would never say "I've been walking at the park", for example, always "in".
You are perhaps thinking of Latin/German, where motion towards something takes accusative and motion from takes ablative/dative.
In this case, the motion is happening in a place, indicated by "w", and is therefore locative (a case relating to a location or place) is used
Actually, i was thinking about another slavic language, the russian language, like in this example: https://forum.duolingo.com/comment/11856389 In which the accusative describes motion of the verb побежать, associated with the preposition в, that i was assuming it would work like "w" in polish in front of a verb of motion. You can see it takes accusative in russian. But that might be not the case in polish, i suppose.
"Rarely do we run in the park" This is the correct translation according to duolingo, at least in my exercise. Could anyone explain me why this "do"?
I agree with this, that 'the correct Polish is more important'. Actually, quite often when I try to think of something in Polish I remember it better by first thinking of the more literal form in English. For example, with the dative case it helps me to add (in my head) words like 'give' before the verb 'help'. Thanks for the reply!