Hello!

As it has been mentioned before living expenses vary quite a bit depending on where you live.
For university you have to pay a comparatively little fee for administrative purposes.
Learning German should not take too long, half a year at the most.

I am wondering though whether you know if your American High School Diploma is accepted in Germany and if you are able to study medicine. Because you may not be admitted to university straight away. It could be that you only have to pass some language exam. However, it could also be possible that you have to take an exam called "Anerkennungsprüfung" or "Feststellunngsprüfung" or even attend a "Studienkolleg" to acquire admittance to university. You can get some basic information on this homepage oder you can call the ZVS (the central institution for admittance to medicine at university) under 0231-10 81 453.

Good luck!