The first sentence is compound, and you know what that means.
The second sentence contains, among other things, a comma splice (a place where two sentences are run together with a comma). Replacing the comma after scrunching sound with a period takes care of that problem.
The handwriting belongs to the friend; therefore, you need an apostrophe to form a possessive: friend’s, not friends.
Her best friend was missing, and nobody had a clue why. She lay on her bed and hugged her pillow, and that’s when she heard it: a scrunching sound. When she looked inside, there was an envelope with her name on it… in her missing friend’s handwriting.
I used an ellipsis in place of the dash at the end because I assume the writer wanted something dramatic. The sentence doesn’t change direction abruptly, though, so a dash is inappropriate, whereas an ellipsis for dramatic pause is. The sentence would also work just fine without any punctuation there.