So I've been thinking about the feasibility of cutting stuff with a thin wire. As the thickness of the wire goes to zero, and the tensile strength goes correspondingly up, does the effort required for cutting actually go to zero?

It seems to me that it can't go to exactly zero, because you still need to counteract whatever forces were holding the material together. But does it go to a small value or a large value, in the case of cutting a strong material like bone? Say, if we tried using a thin wire to decapitate a person standing up, would they actually get decapitated, or would they just fall over?

This might be a dumb question, but is the specific lesson of the Something To Protect article reflected in these last chapters? If so, in what way?

Since HP erased all or nearly all LV/QQ's memories, how is it different from actually killing him?

What would happen if he used the Philosopher's Stone on Voldemort's transfigured form? I guess the transfiguration would become irreversible.

He wants to figure out how to restore Quirrel, but is the risk of accidentally releasing Voldemort worth it?

I though that Death Eaters mostly had only one child, not 2-3.

"Sheila, Flora, and Hestia Carrow. Lost both their parents last night. Students who have lost their fathers include Robert Jugson. Ethan Jugson. Sara Jugson. Michael MacNair. Riley and Randy Rookwood. Lily Lu. Sarah Sproch. Daniel Gibson. Jason Gross. Elsie Ambrose..."

I don't find anything sad about it. The DEs' lives were forfeit anyway. Not refusing to kill a child on command only confirms it.

Also, I imagine that 'night' ('when it's dark out'), is often less than 12 hours of a 24 hour period.

Are you saying you'd like to bet on something? Before you answer:

• The archaic-English saying about the Deathly Hallows looks like a prophecy. And from an out-of-story or Doylist perspective, it could also come true without definitively being one.
• "But like all superpowers, long-range life extension can only be acquired by seeing, with a shock, that some way of getting it is perfectly normal." We can rule out an emergent property of the three Hallows in combination. We can mostly rule out someone breaking the established rules of time travel (though I have to qualify that because I don't know how prophecy works). Whereas the Elder Wand increasing the power of Repair Charms seems pretty normal within the story. We've also established that sufficient reductionism can alter spells.
• As I said in my sibling comment, I think you're wrong about the meaning of the Professor's actions - but let's make a much narrower assumption. Let's say a "Resurrection Stone" manifestation can give Harry facts he doesn't consciously remember. That would likely suffice to tell him about the Wand's abilities or appearance. He might or might not need the Stone to also hint at a simple deduction, one that at least one dead person known to him could probably have made.

"an incredible spell... is it not?"

A few students on the Ravenclaw side were looking indignant, but for the most part the students just looked relieved, and some Slytherins were chuckling.

Quirrell is joking. He doesn't care about the results of the ministry-mandated test, as he already knew what grades his students had earned from him regardless.