near = возле
by = от
In English, Seattle, Washington is near Vancouver, Canada. But it certainly isn't by Vancouver as it is 150 miles away and in a different country necessitating an hour or more delay at the border if you are driving. Few people would say something was by somewhere else if it takes three hours to drive there under optimum conditions.
Duo is teaching you that the difference exists in Russian as well.
You can say that the difference is unimportant to you when speaking in English, but the Duo computer won't let you say that about Russian.
Duo wants to make sure you know the difference between the two words. The only way for them to test you on that is if you reflect the difference in your translation.
What? "Near the café" doesn't sound awkward at all in English. "Nearby the café", however, is totally incorrect grammar. "Close to the café" should be fine.
You also mentioned "near to the café" in another comment. This is certainly awkward, and I don't think it should be accepted.
Theoretically you could say «Мой дом располо́жен бли́зко к кафе́», but this is not the phrase I would use. «Во́зле кафе» sounds better. But I can't explain why, though, sorry!
Кафе is indeclinable, so all its forms (all the cases, both in plural and singular) are the same. This happens with foreign words sometimes.
Is «возле» a preposition that requires genetive? And is «кафе» a foreign word so it should not be declined?