The girl walks by the boy, generally means "the girl walks by the boy (passes by) with her head in the air". I think " the girl walks beside ( or next to) the boy" seems to me a better translation.
Are the στο and στην in these sentences just based on the article of the object?
Στο also covers the usage of "to". I go to the house=πάω στο σπίτι. Few prepositions are accompaigned by genitive, most of them use accusative.
I gave the translation as "the girl walks near the boy" and it said that was wrong and it has to be "next to". Am I wrong? If so, why? Those sound like they mean the same thing to me.
Next to is not the same as near. "Next to" denotes a closer proximity than just "near". My house may be near a mountain, but next to my house there is a bank and a bakery.
Duolingo is giving me "near" as a translation, which is why I used it in the first place. If that's not correct, maybe it should be removed as a translation of δίπλα.
It would be extremely useful to have a longer explanation of the prepositions (and the genitive) in the introductory/explanatory sections. I have not yet come across an explanation for the formation of στο etc. Maybe it is in the Accusative lesson, which I haven't started yet. Also why don't you add a column in the list of prepositions or an explanation about which prepositions are followed by the genitive and which by the accusative. In any case, thanks for the course. It is done amazingly well!