1. Emily saw Laura driving from the pay phone across the street, but the Pin dropped one of Laura's cigarettes from the passenger side window.
2. Most probably it was passed from the Pin to Laura to Dode (though it's possible Laura got it to Dode through Kara.)
4. She told him she had his child, he freaked out. Much like what happened at the tunnel with Dode.
5. Once she knew Brendan had told Trueman about the brick in her locker, there was hard evidence, and she was trapped.
And that's straight from the horse.