Is this data encrypted and can it be obtained by law enforcement?

If that were to happen, I doubt any manner of encryption would help. You are suggesting a dictatorial society would be some how deterred by your iPhone's encryption rather than forcefully and without regard to the law, make you simply give it to them if they wanted it. Or in some way not already have it if we have reached such extremes.

It's called fiction for a reason.

1. Yes, all data in the Health App is encrypted on the iPhone and in the iCloud backup.
2. Yes. Law enforcement can compel you or Apple to provide access to your devices and account if you are suspected of committing a crime through a search warrant signed by a judge. Though not sure what law enforcement may want with your cycle data unless you are planning on running a pregnancy fraud and you get caught of course. Seems like a suspicious question to be asking.

The health app likely wouldn't contain the kind of evidence they would be looking for in a scenario like that. More damning would be location data gathered from your cellular provider, shipping records gathered from the USPS, UPS, FedEx, etc., logs of phone calls from your cellular carrier... the list goes on.

As it stands, the courts have ruled that you can not be compelled to provide the password or passcode necessary to unlock a phone, computer or other digital device. That is one of the reasons that biometric identification like Face ID or Touch ID will 'time out' after a period and require the passcode to be entered.

Of bigger concern would be third-party period tracking apps that may not have the same level of privacy protections that Apple has. They are best avoided now, especially in those states that allow any person to sue you for obtaining certain kinds of health care.