Is "Oni rozumieją się nawzajem" a common expression in Poland? I have never heard of the word "nawzajem" in this context or any other context. The only expression with which I am familiar is "Oni się rozumieją". Do both expressions mean the same thing — or is there a subtle difference?
Nawzajem is a useful word to distinguish the concepts of "themselves" and "each other". Unlike in English, this distinction isn't usually made explicitly, but you have to derive the meaning from context.
In this sentence, nawzajem is indeed optional, as the alternative interpretation "they understand themselves" is quite unlikely.
In other contexts like "oni widzą siebie" it's not that obvious and it's perhaps better to clarify it with an additional word.