Practically speaking, it's impossible to roll 6 one hundred times in a row on fair dice. Not technically impossible, but we each get to calibrate our skepticism based on how far out the probabilities are.

In this case we can be sure the dice aren't fair because there's significant motivation for them not to be, or at least it's easy to imagine a manufacturing defect in the dice.

It's absolutely possible, but it means that you need a lot of good evidence for a 210 IQ to outweigh the odds that the score is a mistake or a lie.

That's right. If the event has a 1 in 390B chance, and there are 8B tries, you would expect to observe the event 2% of the time you conduct the 8B tries. So if you did 8B tries 50 times you would expect it to happen once. And its something higher than 8B - current population isn't the correct sample size.

IQ isn't some intrinsic property that we can measure that has a probability distribution. It's something we construct to have a specific probability distribution. Essentially, you have >145 IQ not because 0.1% people happen to have that high of an IQ but because we define 145 IQ to be the cutoff between the smartest 0.1% of the population and the dumbest 99.9%.

As a consequence, an IQ above ~3 standard deviations is basically unmeasurable with more tests, and by 6 standard deviations I'm not sure is even possible to theoretically construct since I don't think what it's trying to measure can be meaningfully defined to discriminate the order of just 8 people on the entire planet.

It's not impossible, but improbable.