All of them mean 'on the other side of '; it could be a street, pathway for pedestrians e g. in a shopping centre, or even a river : 'across the river (from . .), on the opposite side . .'
'The post office is across the street', 'The café is across the park' : 'from' is omitted as it is understood that it is across from where you are or where you will be.
'The post office is across the street from the market’ ;
'The post office is opposite the market.’ : this information applies whether you are at the market or not. 'Opposite’ could mean across the street, or facing towards the other site, and close to it e g across a pathway, square, etc.