asplake parent
Even with cyclic relationships between types, immutability makes cycles within instances difficult (without laziness anyway). A syntax tree would be a good example.
Yes, and the nice thing about doing it with immutability is you can still have recursive types to build linked lists, trees, and/or dags. From there you can build hash-array-mapped-tries, finger-trees, and so on, giving you friendly dict/list or JSON style data structures.
Yes, either is sufficient, I think.
Edit: I think the common idea with both solutions is that our objects have some weak order (the order in which their types were defined, and the time at which the object was created, respectively), and objects are only allowed to point to objects strictly less than them in this order.