See and 'opposite you' sounds extremely unnatural to me in this context. I agree that 'across from you' is definitely the most natural sounding translation. I think 'opposite you,' 'opposite to you', and 'opposite of you' are all equivalent statements in English, so I was wondering if naprzeciwko has a connotation that JUST means "opposite" and there's something you would add to make it "opposite to/ of".
"Opposite" as in "I am standing opposite you" is a preposition. "Opposite of" and "opposite to" use "opposite" as an adjective. That's the main difference. "Naprzeciwko" is also a preposition so it translates as the English preposition "opposite".
The adjective is normally used to describe an opposite quality, like big being opposite to small, or if we were to say that your opinion on this sentence is opposite to mine. You could technically say that an opposite position is an opposite quality, but I'm fairly sure you're not meant to use it in this particular type of sentence.
The preposition can only be used to mean the position of an object compared to another, as in sentences with meanings like "they sat facing each other [at the table]" or "he lives across [the street] from the hospital". These would be "they sat opposite each other [at the table]" or "he lives opposite the hospital".
'Across from you' is an Americanism, in England it would be 'opposite you' or 'facing you' (if it or you literally turned to face the person/thing), with both meaning only physical position). 'Opposite of you' and 'opposite to you' would mean having opposite physical or other characteristics, or opinions (tall/short, satisfied/angry, in favour / against, etc.) with 'to you' suggesting opposition to something rather than just being something different.
It accepts both dialects and I think that it should—it is impractical to only accept one dialect as this course is for English speakers to learn Polish and both dialects are very close to 100% mutual intelligibility, though I do not think it represents many features of less prolific dialects. I do see where your impression may be coming from—the American flag used for anglophone courses and the Statue of Liberty used for foreign language-English courses—but I am nearly certain that it is only because the American dialect is more prolific and or that Duolingo is based in the United States.
Nah, if the speaker believes something is this or that, it doesn't necessarily mean it should be accepted that way, cos if their grammar leaves much to be desired, there are potentially more natives, who would disagree with the statement the person believed. So let's continue to stick to the rules.
Not really, when denoting something placed diagonally from here, we would(or at least I would :P) rather still use „po drugiej stronie”, as any way you look at it, it is still on the other side of the crossroad.
When the diagonal aspect needs to be stated, „po przekątnej” would be used, but that's a bit technical („przekątna” is the maths term).