The general travel document for transporting professional camera gear across borders is the carnet. A carnet is like an insurance policy that gaurantees what you bring into a country you bring back out again. And, on the US side, the equipment you have with you on your return is not stuff you bought overseas. So no buying or selling gear abroad.
But carnets are really expensive. There’s a steep fee plus a percentage of the value of the gear. When I travel with the big camera we always get one because it’s SO obvious we’re a professional crew. It cuts down on suspicious questions because we’re upfront who we are and what we’re doing. We’re not backdoor import/exporters, we’re a professional video crew. When I travel with a smaller camera I usually don’t bother. It’s taking a risk, but a small one. The EU is pretty friendly. Bring a letter from the hospital you’re shooting at, and if there are any hassles at the border you could show them that.
Note that not all countries accept the carnet. The EU does, but, say, Mexico doesn’t. Do your homework.
The US customs does have a form you can use to register your equipment. It’s free! You list your equipment (with serial #’s and $$ value), get it stamped on your way out, and if you’re hassled on your return you have proof that you left the country with the gear and therefore don’t owe any duty.
As far as power goes, usually battery chargers are dual voltage. Check your gear. All you should need is a plug adapter from the twin blade US plug to the two round prong German plug. Travel stores or Radio Shack will have those. If you’re using lights I wouldn’t fool around with transformers – I’d get 220v lamps for my fixtures and plug adapters for my cords.