I am a native speaker of American English, but I have a bit of international influence. I would not use across by itself in place of opposite, but I might say:
The man across the room was staring at me. (or) The man across from me was staring (at me).
The man you're looking for is in the shop directly/just across the street.
The people in the house across the street never draw their curtains.
I would say that across requires an object. It could be "across the street", "across the way" or "across from me/us/mine/ours". The "opposite" sentences sound fine to me, but I think I would be more likely to use "across" in my own speech. If I used "opposite" I might also add an object: the man opposite me, the house opposite ours.
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