[HAPMCEZ]

Intuitively, yes.

If something is irreversible then it's not 1 to 1 and you don't use the whole state space, so you'll likely have short cycles.

Second part, again yes. But you can add that useful irreversible transform in the finalization of the output, and not in the state transform itself.

I'm self taught so my understanding and terminology may not mesh with the people who have been taught this.