I don't know where you get that the central element can not be $1$, because the Cardan grille does not have any special "requirements" as you're implying. In the original version, a piece of cardboard has several holes cut in it (= the grille) and when it is placed over an innocent looking message, the holes cover all but specific letters spelling out the secret message.
Simpler put: the holes you are cutting, identify the letters of the secret message. The other parts (which are covered) are the text to be ignored.
Let me give you a hint by providing you with a practical example…
The harmless looking, to-be-transmitted message could read:
ALL THOSE TEENIES ARE CRAZY KIDS!
and (taking your boolean $1$ and $0$ approach) the grille could look like this:
then the hidden message would be readable by applying the grille like this:
ALL THOSE TEENIES ARE CRAZY KIDS!
That's all that's to it. So, there are no other requirements but the obvious one: if someone puts the grille on your text, only the hidden message should be readable…
In other words (and to answer your question by the letter): the only requirement of the grille is to have "holes" where the hidden message's letters, numbers, and/or symbols are located, so that when the grille is applied to a harmless looking message (like a letter or book page), the hidden message is the only thing that remains visible because everything else is covered by the grille.
You might want to check Wikipedia's related article if you need another, more classical example.
Looking at your edit, it becomes obvious that there's an additional step you're talking about... meaning we're indeed not talking about a pure "Cardan grille". A pure "Cardan grille" would not touch/change the text the grille is applied to. It's just a paper with holes showing you what letters of the plaintext are the secret message.
The rotating matrix your latest edit shows is something completely different. It could be called a grille cipher, but it's definitely not a Cardan grille… it could be a derived Fleissner grille (also known as "turning grille"), but I would need to be able to check the article you've been reading (see my link-request). It could well be that the article you've been reading talks about multiple grille cyphers; maybe even a combination of them. Until I've read that article , I can only guess… Fleissner grille.
If it's a Fleissner grille (or derivate), you might want to look at this related PDF which explains them (as well as attacks on it). Besides that, this website practically explains the Methods of Transposition as used in the Turning grille, including the center symbol thing you've noticed and are asking about.
You'll notice this image of a turning grille in action also has that 3x3 matrix in it's inner ring.
As for the 3x3 matrix itself, it's logical that if you rotate it around the middle, the symbol at the center will not move/change. Yet, I expect that what your edit shows is just part of multiple steps of remixing the 3x3 matrix. Otherwise, you're indeed correct - the non-changing center symbol would be one of the weakest parts of the matrix-mixing process.
As for the requirements of mixing, rotating and shifting a matrix… that is defined by the individual cipher implementation, not via generalized rules that apply to every cipher.