Biology 101 - S3-E1
Visible crew/equipment: At the beginning of the episode, after Pierce rejoins the group and Jeff and the others begin to leave the room, watch Britta as she stands up. When she turns away from the camera, you can see the actress' microphone-pack in the back of her jeans briefly. (It's hard to spot but it's there, and is confirmed in the commentary track.).
Answer: The implication is that Jeff will still be teaching at Greendale after Annie and Abed leave. As for who became vice dean? It's never shown, since it's not really important to the series.
TedStixon