One thing that's not clear from the article (perhaps it's explained in the book) is why the school had his marriage certificate on file. Since it listed his SS rank and the fact that he worked at a concentration camp, I'm assuming the US immigration authorities did not see it. But then the question is ... clearly he realized that being a Nazi was frowned upon in the US, so why would he provide that document to the school?
The book looks at that document as a sort of smoking gun, too. I think the simplest explanation is that Kulle didn't think the SS thing was a big deal, just a technicality he had to work around to get into the US, and that OPRF (our high school where he worked) didn't really know much about it either. It wasn't unusual for someone to have contemporaneous German documentation --- especially in Chicago, which was a hub for post-war immigration. Gross-Rosen in particular was not well known, even into the 1980s --- the centerpiece of the book is a sort of courtroom drama wherein Kulle's lawyer attempts to convince a judge that there wasn't much of anything untoward about the camp at all.
So the short answer is probably that nobody looked too carefully at Kulle's documentation when he signed on to a low-level janitor's job at a high school.
It's slightly more sinister than that. If you had to be a member of a Nazi organization to get ahead or get the government off your back because you might be viewed as politically unreliable the SS was a common choice. Members would do some paramilitary exercises now and then and be otherwise left alone. For things like Einsatzgruppe or Totenkopf you had to volunteer. The guy knew that well enough.
Yes. Also: that's common knowledge now, but probably wasn't in 1959 (certainly the distinction wasn't apparent in newspaper articles of the time). I don't think it was crazy for OPRF to assume, regardless of any documentation Kulle provided when he was hired, that he'd been vetted at immigration, and wasn't a war criminal. Of course, it was crazy for administrators to come to his defense in 1983 when the details were flushed out! But the village as a whole appears to have wanted him gone.