Great idea, especially since many popular cycle tracking apps have a bad rep of sharing data eagerly with Facebook and other entities. One thing though: I know it's popular in these apps to show the cycle as a "clock face", but if you think about it, this is a weird representation, because of the variations in cycle lengths (of natural cycles not changed by contraceptive hormones). So, if one cycle is 26 days long an…
The issue of lack of exact ability to predict will be an issue no matter what, because the whole point of this app is to help you predict when your next period will start. It doesn't matter if that's displayed as a countdown, or as a calendar, or what.
But perhaps one way to alleviate the "5 minutes to midnight" issue is to have the entire section between, say, 9 and 12 be the potential start of the period, with a less-certain color at the start and a more certain color by 12. For people with a lazier period, the "maybe it will start here" section could be wider, and for people who are super regular it could just clearly show it starting at 12.
For comparing between cycles, it looks like there's a very clear statistics tab with that info.