Hi Adam,
Yes, as you observed, when an income is $0, it automatically becomes an expense. I agree this is slightly confusing. I will file it as a request to make a $0 income possible, by adding an additional flag that indicates whether a budget limit is income/expense, instead of relying on the sign of the number to determine its type.
Regarding the second question, there is currently no support for rolling month-to-month budget. The estimates that are generated based on your past spending may help you get started, but those numbers aren't the ones you enter on your previous budget.
Even though you can setup a one-month budget in Savings, I always recommend my users to create budget for the whole year, because some categories of spending don't occur on a monthly basis. This is what Savings is designed to do, and is why there is no rolling amount option. That said, I will file this as a request for future improvement. I can see how using the previous budget amount is useful even for creating annual budgets.
Hope this helped. I'd love to hear your thoughts.
Yi