Your last statement gives me pause: "And how exactly radio buttons/checkboxes are understood by AT users, because obviously this isn't the supposed behavior of checkboxes/radio buttons."
If you have non-standard behavior for your radios/checkboxes, will the sighted user be confused too?
With 'normal' behaving radios/checkboxes, the AT user will understand them just like a sighted person does - experience. You learn that a radio is a group of mutually exclusive choices whereas a list of checkboxes allows multiple choices. The screen reader will read the role of the object so the AT user will know what to do.
Now, if you're hiding/unhiding objects based on those selections, the AT user needs to be notified. That's typically done with aria-live. By default, an aria-live region will be read if the text changes or an object is added to the DOM which should include being unhidden if you're doing it via display:none. If you unhide by moving an offscreen object to onscreen, or changing the clipping rectangle, or changing the size of the object, aria-live will not help.
Also look at aria-relevant. By default, it's value is 'additions text', which is the behavior I mentioned above. If you need the aria-live region to be read on other conditions, look at the other values of aria-relevant.