Ben’s teacher’s name

Same way you tell everybody else. After you're done with Carley, simply walk down to Clementine and pick "I need to tell you something..." then pick the "I've killed"/"I'm a murderer"/etc. option.

If you take her to Crawford she will:

• stay in the room with Ben for the most time,
• shoot and kill the walker that attacks Molly after you miss your first shot, and
• ask for Ben to be saved, because he is her friend, if you tell her that she has a vote (I said yes) when Ben has his moment of idiocy and tells Kenny he is the one to blame, and his fate is up to debate. This also prompts Christa to revoke her vote.

Furthermore, Omid did not die. I have read but not verified that the walker indeed goes in the house, but should stay in the cupboard where the broomstick falls out.