A: Well, as the Librarian card states, if the Necronomicon is not on the table, then the Librarian card counts as the Necronomicon for Actions and New Rules. Miskatonic Study Group is a New Rule. So, yes, players get to draw and play an extra card on their turn if the Librarian is out. The person who has the Librarian can take the extra bonus of ignoring Hand Limits – again, only if the real Necronomicon is not on the table. If the real Necronomicon is out, everyone will be able to take the general bonus, but only the person with the real Necronomicon gets to ignore Hand Limits.
See also: Does Animator count as the Finger Of God for smiting…