Focal length of Eye of Sauron? Since when is that an optical eye? Isn't it a magical eye or some kind of partially-omniscient remote viewing, combined with awareness of what all his aligned entities are seeing? Even if it were a purely optical eye, and even if he always had line of sight to what he wanted to see, the question has fatal problems. If you assumed an infinite-resolution retina and perfect lens, and if you could exclude field of view over some arbitrary angle like 1° based on the fact that he might not be able to focus on more than one town at a time, what in the text could possibly be used to narrow down whether he has a field of view of 10m or 100m or 1km in any particular case? While we're speculating on an absurd hypothetical eye optics question, how do we even know it's not a compound eye with multiple different focal channels? Stackexchange even comes to the rescue with a quote from Fellowship stating that the eye was a pit opening on nothing (i.e. clearly not an optical eye, as "nothing" excludes a retina), and a comment further stating that the eye had no physical form and was only perceivable to a few people[1].
In that coastline question, what's the definition of shore length (isn't that a single
a scalar) in terms of ocean depth (wouldn't ocean depth be zero at the shore)?
If there's not a given mathematical relationship, the derivative with respect to ocean depth is zero, right? The question is confusing. I get the sense you're reading something else into the question, but it's not clear what. There's no clear definition of the variables shore length or ocean depth, there's no function relating those variables, and if there were a function I don't see why it would be likely to be differentiable.
I'll grant that some of the questions seem half serious and answerable... but mostly only if you have the obscure data necessary to answer them. Does anyone know the statistical distribution of blue whale length, or the armspan of Jesus (is that pre or post crucifixion armspan)? Does anyone know the font and font size used and ink weight and average characters per page and number of pages used by the Times in their print edition? That NYT question could be determined, but would take a fair amount of investigation to get those necessary estimates.
Questions like those are difficult for Wolfram Alpha not because it's too dumb, but because it doesn't have data needed to answer them. Not many humans, if any, have the data or knowledge to answer them either. If the questions were after ballpark figures, then the questions should be littered words like "average" and "typical", but they're not. You have questions about specific species, specific people.
Then, when it really matters, those specifics vanish: When asking the total time needed for everyone (everyone!) to adjust watches during DST changes, assuming everyone has a watch, there's no mention of watch type, or what to do about the few cripples who wouldn't be able to set the watch without assistance; would the total time be infinite then since for a few people the task can never be completed, and the question specifically said everyone, rather than asking about a typical case?
Those are just a few of the most recent questions. Given how quickly those can be torn apart, why is my original assertion even worth debating? That twitter account is, generally speaking, tweeting silly or poorly specified questions that even reasonably intelligent humans couldn't provide definitive answers for.
[1] https://scifi.stackexchange.com/questions/27657/was-the-eye-...