There is no "explanation". These are simply errors. You should not see these in any edited text, but this kind of stumbling over words is not uncommon in unrehearsed speech. The example in the lesson plan is a mistake. I suspect that part of the NY Times website is not as carefully checked as the main news articles and opinion pieces.
The sentence "Why is yawning contagious?" is a correct question. "why yawning is contagious" is a sentence fragment. It is a content clause that could be used like a noun in a sentence: "I'll tell you why yawning is contagious."
It is a mistake to include "is" twice. A native speaker would never do it intentionally. The same goes for all the other examples. They are mistakes.
The first example is more or less meaningless on its own. It can be parsed only when placed in a context.
[What was saleable] [as far as the freak was concerned] [was], of course, physical difference, in a form that was both marketable and palatable.
There is a content clause "what was saleable", which is modified by "as far as the freak was concerned", and this is the subject of the sentence. Then the main verb is "was". Compare this example
The apple that was on the table was red.
The first "was" is the verb in the relative clause "that was on the table". The second "was" is the main verb in the sentence.
The second is probably a mix of "When I found out what a cheapskate she was" and "When I found out she was a cheapskate" But note that neither of these are complete sentences. It could also be part of a longer sentence, with the first part being a content clause, but it's not well written:
[When I found out she was a cheapskate] [was] the day she took all the mini shampoos from the hotel.