I think it always means "that over there", but Duolingo is just translating it to "that" for simplicity purposes. At least, that's the only meaning of 저 I ever learned from my textbook, but I can't say for sure since I'm not a native speaker
if the sentences had a better grammar and like a... i don't know, maybe a more meaningful sentences it would have been amazing app. it was fun at the beginning but i don't think i can learn Korean that way with bad grammar and super weird sentences
Are you a new user? DL is notorious for coming up with "super weird sentences". That doesn't mean you can't learn anything here. This app may have glitches in grammar but the essence of it is to teach you proper syntax.