"The bag is near the table."
Translation:Сумка возле стола.
I think she meant that because the subject is "the bag" and not "a bag" we are talking here about a defined subject. We know which bag is referred to and the sentence is about the location of that particular bag; therefore the emphasis is on the table, which is what is put at the end. Whereas, if it had been "a bag", we would be talking about any bag and so the sentence would be about what is next to the table, in which case the emphasis would be about the bag and the structure with the locatif complement coming first is the one which would apply. Grammatically, both are correct but i guess Duo forces us to translate that way so that we understand the difference.
You're thinking of на = "on" whose objects take prepositional case when static location is involved. Objects of the preposition возле take genitive case. It's just something to memorize.
Note: When motion is involved, objects of на are in accusative case, as in Я кладу посуду на стол = "I put/place the dishes on the table"
Yup, that's what I've found.
See either of the comments above in this list by Jeffrey855877. (or some of the other comments). Often it is useful to see if the prior responses have addressed your question already, or for that matter to see if there are other issues with a given example that you hadn't previously considered.