German Healthcare for Unemployed (Munich)

Good Day All :-)

In May of this year I moved,along with my German boyfriend (Who has a Job in Germany) , from South Africa to Munich, Germany (I have a Swedish-EU Passport).
I have been on a ferocious Job hunt for a while now but the process has proved harder than I thought, especially as I´m not business fluent in German.
My South African Medical Aid covers me internationally for 90 days out of the country,after that I have no cover whatsoever-unless I return to SA.I was hoping to find a job in Germany within the 3 months, which would then automatically allow me to register for German Healthcare . A recent €350 uninsured trip to the emergency room for torn ligaments has further amplified this worry.

My question is: Currently Im still unemployed (still on the hunt though) and will have no health Insurance whatsoever from 1 August. What are the options available to me in terms of getting medical cover in Germany until I find a Job. I really dont want to be in the situation where some thing life threatening happens and i have no medical care.
Am I able to Join German Public healthcare system even though Im unemployed?

Would I Have to /am I able to Take private health Insurance? If so does anyone have good recommendations for companies and will I be able to go onto the public plan once im employed?

Any Swedes out there that know whether i can get access to the Swedish Healthcare System as im a swedish citizen, however never lived there, and if this would be valid Throughout Europe?

Any assistance with this would be greatly appreciated, Ive tried many sources as well as asking people who dont seem to be able to help as never been through situation.