Seems to me the force needed to penetrate tracks the diameter, but the strength tracks the area of the cross-section.
That is, decrease the thickness by N and it decreases the force needed by N but the strength by N squared.
Below a critical thickness, the wire would just break.
Spiderwebs don't slice you up if you run into them.

I think it's pretty obvious.
Voldemort has always been attracted to power, and it's well known that Hermione is the most powerful witch of her generation.
He made several overtures to her, but was unable to turn her from her path, and so he killed her.
Upon her death he felt great remorse (such was his passion) and decided to bring her back from the dead (such was his power).
Dumbledore tried to stop him, and so was eliminated.
In fact, Voldemort was so enamored of Hermione, that after she was brought back, he use dark magics to give her even greater power.
Quirrell (who has been hiding his identity of David Monroe) was secretly on hand for the ceremony, but by the time he realized what was happening, it was too late to stop it.
Cutting charms were used on Voldemort's hands, and other terrible damage, but despite all this, Quirrell was defeated.
Ironically, having given her the power of friendship, it was the power of friendship which ultimately was his downfall.

I notice you are confused. I think you've made two questionable assumptions;

Assumption 1. Wizard Children are not generally treated as competent at age 11.

Assumption 2. The children making the announcement at Hogwarts are responsible for brokering the deal. I.e. they aren't just mouthpieces for their respective families.

Assumption 2b. The Hogwarts staff is aware of 2.

Assumption 1 might be true - but I note that the age of majority has been increasing over time, and wizarding society is in many ways old timey. It seems reasonable to me that allowing a child of 12 to command a wizarding army is no stranger in wizard society than allowing David Farragut to command a ship at age 12 was during the war of 1812. Also, we haven't seen the reactions of the wizarding world in general - maybe everyone who isn't on the Hogwarts staff is scandalized. For that matter, maybe the staff is too, they're just not openly scandalized.

But assumption 2 seems completely wrong to me, and likely the main source of the confusion.

True Patronus couldn't look like a snake.

I see no justification for that statement. Perhaps True Patronuses can't take the form of an animal, but that says nothing about what they can look like.

Would a sentient snake wizard say a True Patronus can't look like an ape?

Well, it's probably supposed to be spelled "Momroe" as in "David Troll Momroe". :)

It's spelled "Monroe" in Chapter 86, and there's a "Most Ancient House of Monroe". Personally, I never get these names right either, but I keep a text file handy with all the names, and hard to spell spells like Legilimency Occlumency Occlumens, and Legilimens. Then it's just a simple matter of cut and paste.

Quirrell's dash to the scene ... indicate that they are afraid of what this experience will do to Harry.

It seems more likely to me that Quirrell's dash was primarily for the purpose of burning holes in Hogwarts. Despite leaving before Harry, and Harry stopping to pick up the twins and stopping at the library, and supposedly making a more direct route, Quirrell still failed to arrive before Harry, or for that matter, at all.

I'm not saying Quirrell is unafraid of what this experience will do to Harry, just that I don't believe Quirrell's dash is evidence of that.

There's a scam I've heard of;

Mallet, a notorious swindler, picks 10 stocks and generates all 1024 permutations of "stock will go up" vs. "stock will go down" predictions. He then gives his predictions to 1024 different investors. One of the investors receive a perfect, 10 out 10 prediction sheet and is (Mallet hopes) convinced Mallet is a stock picking genius.

Since it's related to the Texas sharpshooter fallacy, I'm tempted to call this the Texas stock-picking scam, but I was wondering if anyone knew a "proper" name for it, and/or any analysis of the scam.

There is a contradiction here between "lucky" and "coin flip". Why does he get lucky on Earth?

I don't see the contradiction. C-Omega tries the same con on billions and billions of planets, and it happens that out of those billions of trials, on Earth his predictions all came true.

Asking why Earth is rather like asking why Regina Jackson won the lottery - it was bound to happen somewhere, where ever that was you could ask the same question.

In the original problem Omega runs a simulation of you, which is equivalent to T-Omega.

I could not find the word "simulation" mentioned in any of the summaries nor the full restatements that are found on LessWrong, in particular Newcomb's problem. Nor was I able to find that word in the formulation as it appeared in Martin Gardner's column published in Scientific American, nor in the rec.puzzles archive. Perhaps it went by some other term?

Can you cite something that mentions simulation as the method used (or for that matter, explicitly states any method Omega uses)?

Consider the following two mechanisms for a Newcomb-like problem.

A. T-Omega offers you the one or two box choice. You know that T-Omega used a time machine to see if you picked one or two boxes, and used that information to place/not place the million dollars.

B. C-Omega offers you the one or two box choice. You know that C-Omega is con man, that pretends great predictive powers on each planet he visits. Usually he fails, but on Earth he gets lucky. C-Omega uses a coin flip to place/not place the million dollars.

I claim the correct choice is to one box T-Omega, and two box C-Omega.

Can someone explain how it is in the “original” problem?
That is, what mechanism does the “real” Omega use for making his decision?

on 3; From chapter 6

As his hand touched the back door's handle, he heard a last whisper from behind him.

"Hermione Granger."

"What?" Harry said, his hand still on the door.

"Look for a first-year girl named Hermione Granger on the train to Hogwarts."

"Who is she?"

There was no answer, and when Harry turned around, Professor McGonagall was gone.

Seems clear to me that the whisper came from McGonagall - Harry was talking to her, Harry turned his back and heard a whisper from "her" that sounded like her. Harry thinks so to - in chapter 8 we have;

The boy's mouth was hanging open. "Were you told to wait for Harry Potter on the train to Hogwarts, or something like that?"

"No," Hermione said. "Who told you about me? "

"Professor McGonagall and I believe I see why.