Will a Python dict with integers as keys be naturally sorted?

No, Python dictionaries do not have inherent ordering, regardless of the key values. If you need ordering, stick to arrays or lists, or better yet - check out pandas, which will allow a similar ability to dictionaries to call by key value, as well as many other powerful features (http://pandas.pydata.org/pandas-docs/stable/10min.html).

In short, no. I'm betting you noted that dictionaries use the hashes of keys as indexes in to an array, and since ints hash to their own values, you inferred that inserted values would end up in order by key if their keys are integers. While the first 2 parts of that statement are true, the inference is not, even as an undocumented side effect. The dict keys are derived from the hashes of the keys, but are not the complete hashes. This means even with integer keys, you can still get out of order inserts since 2 values could collide at the same location (or even have "out of order" hash-derived values) and thus end up inserting the keys out of order in the dict.

Basically, think of it as the index in the internal storage array of the dict being some number of low order bits from the key's hash. Just because one number is larger than another doesn't mean that a value built from it's truncated low order bits is going to be larger, or even different.

No, you cannot. Always sort if you want to iterate in an ordered fashion.