If the gunshots were all blanks and squibs, then how the tire on the (fake) private investigator's car get blown out by the gunshot? They would have had to known in advance that (a)Nicholas Van Orton would have confronted the private investigator (b)he would have stolen the gun (c)he would have shot the gun and (d)he would have shot it at the tire.
They could've just guessed he might do that. The PI could've been wearing a squib shirt too. The point is, it was entirely optional. It wasn't necessary to that scene that he take the gun and shoot anything, just that he think someone had sent a PI after him.
Perhaps the gun was loaded with live rounds. They would not have expected Van Orton to actually shoot someone, and he didn't.
If the gunshots were all blanks and squibs, then how did the car window get bullet holes in it?
You answered your own question, blanks are what makes the muzzle flash from the gun, and squibs are the bullet "hits". They likely used the exact same method as a movie shoot would.
How did they know what part of the building he would jump from?
It's a bit of a stretch, but Feingold mentions that if he hadn't jumped at all, he was supposed to throw him off. If Nick had wandered toward the wrong part of the roof in a suicidal daze — and they had enough of his actions planned already — he probably could have caught him and gotten him back on the rails.
The Mind Experiment:
As soon as you forgot it you're playing. As soon as you think about it you lose. Loss must be announced. What happens if you break a rule?
You lose. Duh.
You seem to be forgetting the fact that the one possible option in the game is to lose it.
If you break a rule, like not announcing a loss, then you "cheated", which is worse than losing, morally speaking.
Not if you interpret it as just not ruining the game for everyone around you.
The rule is, you have to announce it. If you do, it doesn't count as a loss for the people you announce it to. If you don't, there's no real consequences, but you'll know you cheated.
Of course everyone you announce it to loses, As soon as you mention the Game to anyone who knows about it, they lose. And I lost when I saw the Head Line for the Headscratcher too.