No, why would they? If you are a clockwork regular then it’s every 28 days, so you get 13 a year. But a lot of people are irregular and or sometimes skip one. So ymmv

They are strictly triggered by a full moon, where do you think the werewolf story started?

Nope. For most people who menstruate, they’re about every 28 days, but there’s a lot of factors involved. Stress during different phases of your cycle can make your period come either early or late. Some people have wildly irregular periods and can go months without a period, some people have cycle lengths that vary more than the general average of 9 days (so maybe one cycle is 29 days, then the next is 38, then the next is 20.) There’s a lot of variation, some of which is benign, some of which can be a symptom of an underlying condition that can be debilitating or dangerous.

But it’s called “that time of the month” because, like the full moon, there’s usually about one a month, and then once in a blue moon, there’s two.

(Also, the length of months hasn’t always been standardizes in the same way. How different cultures throughout history have broken down and do still break down the year into different intervals is fascinating. For example, some calendars will break the year down by lunar cycles – the term “month” is a cognate of “moon” – and end the year after 12 lunar cycles, while a solar year will end the year after a full revolution of the earth around the sun and break the months down into twelve months around that without consideration for the phases of the moon, while lunisolar calendars will try to reconcile the two by having lunar months and throwing an extra month in every few years to keep things in sync with the sun. You can read more about it here: en.wikipedia.org/wiki/List_of_calendars )

TL;DR: No, it’s not exactly once a month. It’s just roughly once a month for most people most of the time, and casual language is imprecise, so it gets called that time of the month.

Yes uteruses utilize NTPoAC (an unofficial spec that is defacto-standard in industry, roughly implementating of rfc5905 using rfc2549). This makes women’s periods synchronize when peering to correct for internal clock differences. The individual unit isn’t guaranteed to be exactly 12 times per year due to latency variation and peer graph discrepancies, but the count is monotonic and regular on average, resulting in amortized constant time complexity which works out to be approximately 12±0.03 in practice, as observed in real world applications.