The Lemony Site - Lemony Snicket: The Unauthorized Autobiography

Lemony Snicket:
The Unauthorized Autobiography

Snicket Sister

(UA.75-76) Ms. Snicket wrote this note which features the following information:
The archives of the Daily Punctillio were stacked in large towers along a street in Paltryville (see also "The Miserable Mill").

(UA.97) "You [Lemony] must not telephone K . . . We are all in terrible danger and thus must not communicate for a very long time."
Here, 'K' is listed with Daniel Handler and Beatrice, and is therefore someone very important to Lemony.

(UA.129) Ms. K began teaching at Prufrock Prep after the retirement of Mr. Remora. She worked there while Carmelita Spats was still attending the school, but was fired after Mr. and Mrs. Spats sent a Daily Punctillio article by Geraldine Julienne to Vice Principal Nero about the dangers of allowing children to read books.

(UA.130) After being fired from Prufrock Prep, Ms. K recruited two orphans into VFD.

(UA.142) The photo's association with Prufrock Prep leads me to believe that the circled woman is Ms. K (and not Beatrice).

(UA.196-97) The Snicket family tree is just too confusing! I'm guessing that J, K and L are Jacques, his sister, and Lemony.
Is the O branch with a noose Olaf? If so, then the Baudelaires are distantly related to the Snickets.
Where is Jacob, Lemony's father?
Lsanbell says: "The bigger bough that J, K, and L meld into is E. E stands for Elwyn, as it says in The Wide Window. I'm guessing that the name everyone called him, Jacob was his middle name or one of those nicknames that don't have to do with anything."
What's up with the imagery? The owl, I suppose, connotes the intelligence of the family members on that bough. Or they like to stay up late and have good night vision. Or maybe the illustrator was just trying to be spooky.
If B's whereabouts are uninteresting, why is there a woodpecker attacking B's branch? Do woodpecker's only peck into dead wood? I wasn't able to find a definite answer online.
Who or what do the eyes lurking in the tree's trunk belong to? Does this have anything to do with why A's whereabouts are unknown?
Finally, what's up with the oh-so-ominous ax leaning against the base of the tree?

The Unauthorized Autobiography

Lemony Snicket:The Unauthorized Autobiography Snicket Sister

Lemony Snicket:
The Unauthorized Autobiography

Snicket Sister