I will throw in several predictions. I myself am not completely confident of some of those.
Time-turners, prophecies and similar devices, which predict that something will happen, work by exerting some mind control upon people in the form of unexplicable urges, such as the urge to take the left turn this one time. I'm not sure how far can they go in order to fulfill themselves.
The events in the magical world are not just dictated by the already-discovered laws of physics, but also by the laws of fairy tales. Dumbledore is pretty damn rational, at many points more rational than Harry (he might even be more rational overall). His reasons for having an evil Potions master aren't simply because this happens in fairy tales. The Universe liked it more if that was the case, so he was probably represented with an evil person who is highly suitable for the Potions position, or something like that. Dumbledore is most probably aware of this law. After Harry case the true Patronus and Quirrell asked him where he'd hide something, Harry gives 5 places: volcano, inside earth, deep in the ocean, somewhere in the air, and in space. Fire, Earth, Water, Air, space-thingy. He can't have said that by coincidence, and this is evidence of that law existing. Quirrell's reaction indicates he's aware of the law.
Part of Voldemort is in Harry. The Sorting Hat either lied, or more likely, Voldemort isn't in his scar - Harry asked about his scar (I realized that much before it was reminded in chapter 90 or 91 and therefore have read a lot of HPMOR with that in mind), but it may still be inside Harry, just not in the scar. Evidence: his unusual 26-hour sleep cycle was probably inherited; he is exceptionally intelligent, and just 11, while his parents aren't particularly intelligent (intelligence is usually mostly inherited genetically); he is better with a broomstick than children who have used broomsticks before going to Hogwarts; his dark side seeks destruction (Voldemort appears to seek destruction too), and is very cold (from his flashback, Voldemort's voice is really quite cold). This probably happened by accident, rather than as a plot - it may be explained with the law from 2. - Voldemort tried to kill Harry, the universe interfered in the simplest possible way, although I'm surprised as to why did the universe let Voltemort find Harry in the first place then.
Quirrell is not Voldemort. I'm still very perplexed by Quirrell, but it would make an awful, predictable plot to have him be Voldemort. He does appear to be a Dark wizard, the Monroe story seems implausible (he doesn't believe in others' love, why would he be a hero? Unless he did that for himself). He probably has a lot to do with Voldemort, but they were neither friends nor enemies. I don't know about the sense of doom, but it probably is connected with what happened when Harry's parents died. It appears that Quirrell doesn't know about it, either - therefore it is probably because he could not see an explanation, because the explanation involves love, and isn't obvious.
Voldemort is the one who will (at least try to) TEAR APART THE VERY STARS FROM HEAVEN. He seems to be all about destruction, though I'm not sure why, and I'm not sure why does he not take the shortcuts Harry had in mind, and this is the weak part of this prediction. Perhaps it is the universe's will that people must die for a good reason, rather than having the world's strongest wizards destroyed by a handful of highly toxic molecules each.
Magic is like that because it is made by humans. This is probably obvious - magic came to exist by humans, this is why a lot of it only make sense in terms of human intuitions, and not so much sense in terms of laws of physics. I'm still very puzzled by the fact that it appears to violate the laws of physics. It also sounded like magic might be a superintelligent AI, but I forgot my arguments for that.
I also wonder, what would happen if you use a time-turner to do the impossible, for example talk to your older copy, so when you see the newer copy, don't time-turn. Would it turn out that someone strongly felt like approaching you while Polyjuiced as you? Is it that nobody would ever think of that in the wizarding world? I'm sure there's a lot more going on with time-turners.
I'm surprised to see everyone overlook the most obvious possibility: Voldemort.
Point one: The earlier prophecy was probably about the same person, and he hadn't arrived yet at the moment. Even if it was about something different. 'he has come' in the last prophecy implies that he had just arrived.
Point two: Voldemort appears to love destruction. I still don't know how someone as intelligent as him hadn't killed everyone in the ways Harry thought of -. Harry's intent to kill, which is presumably very Voldemort-like, is extremely creative and effective even at his magic level and age. But assuming that Voldemort is about destruction, he might want to end the world.
Quirrell or someone (e.g. Snape) might have resurrected Voldemort right after stealing the Philosopher's Stone - a time-turner may be involved.. Dumbledore was away, Snape might be unreliable, it could have easily happened. A counterindicator is that Dumbledore is probably also aware of this risk, and therefore might have taken counter-measurements, although we can see that Quirrell can fool him in the part where he learns about the zoomagus potion left in Bellatrix's cell (though it portrays himself and Snape as significantly inferior to Voldemort and Quirrell, so I'm reluctant to believe it was real, rather than them acting in front of McGonagall).
It doesn't fit my model of human behavior. But that's possibly just me.
I'd imagine that if Snape got really angry, but it's only because Harry offended him without knowing, well, he wouldn't be close to harming him. I guess it would be appropriate to say "you almost died" if it's not true, but then Harry acted as if Snape might reconsider his decision to not kill him, rather than being just apologetic, or something like that. Or maybe he was indeed, and I am likely to be underestimating the strength of the impact that Harry's words had on Snape.
But if others interpreted it like me, then I got it right. Hmm.
There was something that has always been bugging me. It's actually several things I don't understand.
When Snape says "You almost died today, Potter", what does he mean? Maybe it's because I'm not a native speaker, but I can't understand that part. My best guess is that Snape got so upset with what Harry said that he almost killed him in his rage. But that seems very counterintuitive to me.
Second, Snape had possibly changed after his conversation with Harry? Does this mean that Snape took Harry's words and thought that Lily is actually not worth his love, after all these years? That's my best hypothesis, but I find it very weird.
Third, did I actually properly understood that he still loves her, after more than 11 years have passed? This is very unrealistic, people get over things, and I suspect that either EY is being unrealistic here, or Snape is simply lying.
Edit: I retract the last part. Still, this does not mean that now I believe this to be realistic, but rather that it might possibly be realistic. Also that EY could indeed have decided to just go with the canon, and I see good reasons for that.
I'd love to see a list of spoilers about things that were hinted at and reasonably sounding hypotheses, if anyone ever made one. Please do reply to this post with your discoveries and speculations. I'm also going to post mine, once I finish rereading HPMOR.
I did notice the title didn't sound right to me. But I also couldn't find the right words (English isn't my native language). Any suggestions?
It strongly depends on the person, some are faster than others.
JCTI takes at least an hour for nearly all people with high scores. 2-3 hours isn't too much.
CFNSE takes 2 to 5 hours, according to the estimation on the website - it's an accurate estimation IMO. A possible strategy is to do it "quickly" (for 2-5 hours or so) and leave everything you couldn't answer definitely for the last. Then spend 30-60 minutes on each of those. I think this isn't going to artificially inflate your score, and I'm quite certain that someone with 100-110 IQ can't figure out the patterns for any of the hardest questions, even if he spends hours/days on each.
Fortunately, we can still view individual replies.