Cross = to move, pass, or extend from one side to the other side of (a street, river, etc.). I had to CROSS the street to go to the museum.
Across = from one side to the other. It is used on the surface and not inside of something.
Through = to reach to the end. It is used when going inside of something
1. At that moment I was walking ACROSS the road. ( on the surface of something)
2.She climbed THROUGH the hole in the roof.( it is inside something )