The maximum monthly payment you can have for german public health insurance is 14.6% of 4.687,50 EUR per month in 2020 - that's about 800USD. Mind you, maximum, not average.

14.6% of your wage is the health insurance deductible, 4.687,50 EUR is the so-called "Beitragsbemessungsgrenze", that is the cap from which on your wage is free - it's regularly adjusted (upwards usually).

You can reach that maximum if you are self employed and voluntarily member of the public health insurance - meaning you have to pay both the employers and the employees share. If you're employed, your employer pays about half of it.

Your chosen health insurance can optionally add an extra fee, usually less than a percent or two, most are free.

How does this work if you're unemployed? Is there a separate public option? Or do you just keep on with whatever you may have had before, without paying?

Also, that "maximum/wage" thing - is that per person, or for a household (spouse/kids/etc)?

The level of care is independent of your payment, if you're unemployed you're still covered without payment, students are covered for free until they're 27 (there are ways to loose coverage, but just being unemployed is not one). Like the sibling comment pointed out: if you're living of savings, there's a minimum payment.

The cap is per wage, so every person earning a wage gets the same cap applied to their individual income. (one of the ways that households with a single high earner profit, while two people earning a moderate wage have less). No bonus for kids here, buy if you're member of the public health insurance, your kid is covered for free.

If you're on unemployment or welfare payments the state pays for you. If you live off savings and don't have income you can pay a base rate (a little bit below 200€).

National average is around 3800. Minimum is 1584, I think.