Harry gets a dull ache in his head (throbbing) when he accepts the gem from his mother while soulgazing Thomas.  The gem contains insight (knowledge).

Yes.  I noticed that in a recent reread.  "you don't gain knowledge without a little pain,"  Harry has 3 incorporeal entities in his head, or is it only2?
1 Lash, 2 Parasite and 2 Mother's Advice
1 Lash the Parasite and 2  Mother's Advice
1 Mother's Advice the parasite and 2  Lash
Not to mention Mab and Molly both have tinkered around in Harry's head.  HH is getting crowded.

1 ) Harry usually has a few supporting characters in each book.  Who do you think will be the main sidekick in Cold Days and in what way will they help?  Who else will have a significant contribution to the plot?
Sith will be the reluctant Pancho.  Toot Toot and Sith snark a lot.
2 ) At the end of Ghost Story, Harry has said goodbye to all his friends in Chicago.
a.   Who will be the first friend to find out Harry isn't dead?
Carlos
b.   What shenanigans/snark will Harry use when he "re-appears"?
Carlos is about to ambush Molly at the order of Merlin, but Harry steps out of shadow, and says “I think not.” And something about bottlecaps, like “you don’t get to be Winter Knight by collecting bottle caps.”
c.   Who will have the coolest reaction?
Morty will have an even cooler & more hysterical reaction than when Harry the Ghost visited him.  Especially since he and Murphy are now living together. Well, his house did burn down. And Murphy could use a change from bad boys like Kincaid.
d.   Who will have the most touching reaction?
Obviously, Mouse.  What’s more touching than a boy and his dog reunited?
Mister will be aloof with Harry but will slap Sith across the room out of jealousy.
3 ) In nearly every book, Harry usually comes up with a new powerup/tool/way of making things go boom.  Given that he just became the new WK, what new abilities will he rely on and which new ability will be most useful to him during the story (and how)?
The shotgun shown on the cover is a  multipurpose tool—flame thrower, staff, cudgel All in one.  But it’s a misdirection.  Harry’s  new tattoos pack a lot of real power .  They won’t fall off like those rings and bracelets.  Or freeze his skin in Winter.
4 ) Harry generally has a "Big Bad" to worry about.  In fact, according to the blurb, Harry is going after someone very specific.  Who will that enemy be, and how will Harry take him/her/it down?
Mab sends Harry after that dragon. She wants whatever his present at the party when Lea received the athame.
 5 ) Harry usually faces some sort of "Choice" in every book.  A point where the easy way out will cost his soul/humanity in some way. According to the blurb, this book will be no different.  What will be the most crucial "choice" Harry makes?
Harry must choose between a long range objective and letting a loved one die.  Personally I’m hoping Ebenezer bites the dust.    Harry could have saved granddad easy enough but the other option was more essential to saving the world.

6 ) As the new Winter Knight, Harry is pretty much garunteed to encounter his Summer counterpart -- Fix.  What will their interactions be?  Will Fix survive?
]Fix and Harry have a beer and grumble about their job duties.  Fix survives the hangover.
7 ) Jim has mentioned that it's about time now to start revealing some of the motivations/dealings of the shadowy figures working behind the scenes (i.e. what Harry calls the "Black Council").  What Black Council secrets/actions will be revealed in this book?
It goes back to the period when Margaret was young, when the Merlin sent the wardens after her.   Margaret then decides to have a child who will be powerful enough to fight whatever the Black Council is planning. 
8 ) There are many WAG ("Wild A$$ Guess") theories on the boards.  Write up to three WAG theories you believe are correct that will be confirmed (or at least have evidence in favor of) in Cold Days.
1.    LC was repaired by subconscious Harry after Lash informed him of the problem.  Our Harry was just sleepwalking.

9 ) Extra credit:  Write down any prediction about that you think might improve your final score.  Only issues aluded to withi n Cold Days will be counted.
I really hope the “parasite” Mab referred to is Lash but I fear that in those missing minutes, before all the Red Court vamps died, that one bit Harry and he now has a spiritual parasite Hunger. Lash and the Hunger snark a lot. Subconscious Harry drinks a lot.
Harry visits the tomb of Susan and the sale of Kleenex skyrockets. 
Before Ebenezer dies he tells Harry that the Merlin is his other grandfather.   Ebenezer married the Merlin’s daughter and kept Margaret’s birth a secret from the Merlin.  Martha Liberty was the midwife. And Margaret's mother.

Has anyone mentioned Harry's invisible lady friend?  The one who guided his hand to his amulet in Storm Front and who Harry periodically smells--most recently in Changes at the church?