As the others have said, the second sentence should be "There's a shop on the opposite side of the street."
When talking about physical positions, across and opposite can both be used for the same thing, but the way you word the sentence is different.
"There's a shop across the street."
"There's a shop across the street from the church."
"Across the street from the church, there's a shop."
With 'across', you need to mention what you need to cross (the street), but you can leave where you are (the church) implied.
"There's a shop on the opposite side of the street."
"There's a shop opposite the church."
"Opposite the church, there's a shop."
With 'opposite', you either need to mention where you are (the church) and leave the thing you're crossing implied, or you say it's on the opposite side of the thing you're crossing (the street).
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Opposite can be used for things other than position though.
For example, 'yes' is the opposite of 'no'.
'Up' is the opposite of 'down'.
'Light' is the opposite of 'dark'.
You would not use 'across' for this purpose..