I'd like to set up Kate so that, if I open, for example, a C++ file, all classes it contains are folded? But not only the root levels, when I unfold a class, I'd like methods inside it to be initially folded too. Etc. Is it possible?
From what I'm seeing, you won't be able to achieve this without modifying the kate's code. I would suggest putting in a formal feature request (a wish) on their tracking system.
It's a feature that I would want as well :)