Here are the completed sentences with the correct phrases:
Alan came across a mysterious map in his grandmother's attic. (found by chance)
It was Will who came up with the idea of going into the haunted house. (thought of)
After getting caught in the rain, Jane came down with a terrible cold. (got)
Stephen King's new book has just come out (become available to the public)
As soon as I stepped into the creepy house, a strange feeling came over me. (affected me strongly)