After recent events I've been looking at jobs in Germany, so this is a timely post. As I understand it some kind of healthcare insurance is mandatory, but most people are part of the government run scheme that's paid for by your employer. If you earn beyond a certain amount you're required to buy private insurance.
Where this leaves you if you're doing voluntary work I've no idea. It may be that you have no choice but to pay the full amount for private insurance, but have you asked The Red Cross? After all they are The Red Cross. They may have it covered.
The old EHIC card will cover you for a temporary stay, but how long "temporary" is is not clear, and that probably won't cover anything non-urgent - i.e. treatment for chronic conditions. And of course that may be subject to the UK staying in the EU...
But everything I've read says that healthcare in Germany is infinitely superior to our own, so in all likeliness you'll get much better treatment. My family in France tell me astonishing stories of seeing doctors the same day; not waiting weeks for test results, and getting treatments done quickly that the NHS won't do it all.
