Does iterating over the same set in Python guarantee me to have the exact same order (providing that it is the same set: I won't modify it between the two iterations), or should I convert the set to a list first, and iterate over the list?
Python's dicts and sets are stable, that is, if you iterate over them without changing them they are guaranteed to give you the same order. This is from the documentation on dicts:
Keys and values are iterated over in an arbitrary order which is non-random, varies across Python implementations, and depends on the dictionary’s history of insertions and deletions. If keys, values and items views are iterated over with no intervening modifications to the dictionary, the order of items will directly correspond.