The next two peculiarities aren't with the Crown but the (Hungarian) Wikipee articles about the Crown.
I'm gonna take the simpler one first.

A Hungarian noble, certain Révay Péter, who hold an important office leading a county, was trusted as a Crown Guard at the dawn of the 17th century. He was there with Mathias II when he was crowned in 1608. This guy wrote a book about the Holy Crown, with the KC-tier title of De sacrae coronae regni Hungariae ortu, virtute, victoria, fortuna, annos ultra DC clarissimae brevis commentarius which was published in Augsburg, 1613. It was re-published a few times since proved to be a very popular work, I think on the Hungary only the Bible ranked more popular than this. The topic of this book is more of the spiritual and judicial work than an analysis of the Crown as an item or piece of art.
The book contains however a very concise description which became of the basis of certain speculations. "Official" researchers dismiss his book as a source since his description isn't clear and he seemed to made some mistakes. However his book came with an illustration, a depiction of the Crown which looks quite different from the real one.
Here's a screenshot of the Hungarian Wiki page which compares the drawing in the book and a later one from 1790. And the subtitle says: "Révay's drawing of the crown (above) and the depiction based on the official inspection of 1790 (below)"
The problem is that it isn't Révay's drawing. Originally it is an engraving made by a German artist, a certain Wolfgang Kilian (https://en.wikipedia.org/wiki/Wolfgang_Kilian), who had never seen the crown, and only could use the little what Révay wrote.
Also there isn't just one but some (all?) later editions use another illustration which is very similar to the first one but still contain a few differing details.
So why the Wiki says it was made by Révay?