The newspaper article near the beginning showed Ollie's last name as Wasmund, but when Emily broke into his laptop later on, the email to him from his partner Aaron showed his last name as Miller.
Emily cried several times after her father's death, but there were actual tears on her face only once. During the other times, when Claire consoled her, they were face to face, so Claire should have noticed her eyes were dry and she was only pretending to cry.
Emily set up Ollie as having an affair with Pam by writing and sending the fake email and texts from Pam to him, but she would not have been able to text fake messages to his phone from Pam without having access to Pam's phone, and she never did, so it was not possible for those "affair" texts to be on his phone from Pam.