I think with the phrases like 'a kind of' or 'a sort of', what comes after need not have an article like here:

a kind of mental illness

a sort of mental illness

My dictionary seems to say 'illness' is countable and thus, I think you can say 'an illness' or 'three illnesses'. Would I be able to put any adjective between, except those that indicate numbers between 'a' and the above words 'kind' and 'sort' and maintain the article-freeness?

a situation-changing kind of mental illness

Then I am confused about the phrase 'a form of'. Are the sentences with the phrase need not concern with an article like the ones above?

a new form of mental illness

a normal form of Christian practice
I see no need for indefinite articles there.
a sort of
this is informal, not for papers