I agree with everything that the above three have noted. Nut allergies are definitely not as widespread or commonly known, and one is expected to take responsibility oneself. Don't expect to find things labelled in quite the same way as in America. Since OP asked about cultural differences, I will agree with Masterphil and say that one is definitely expected to take responsibility for oneself, and that there really isn't as much incidence and thus awareness of food allergies in Germany as in America.
And as noted, please remember that in many areas 'American' English is not so easily understood. Not only is the accent different, but the actual words in the vocubulary are quite different. I myself speak differently when in America than I do when in the UK (or almost anywhere else in the world where English is generally well understood). While you may be coming to a corner of the country somewhat still populated with Americans and still somewhat geared towards Americans, it is also still a very rural area and you may well encounter people who do not speak English, or very little.
I don't think that it is quite so different anymore, but years ago the ingredients in Austria vs Germany were quite different on many packaged goods (similar to Germany vs America) In fact, many Austrians would cross the border to purchase the German version of certain products as a result. But with EU regulations I don't think that the differences are as widespread and labelling is generally much more consistent.
Here is a thread from a few years ago which may be of some use
http://www.flyertalk.com/forum/germa...t-airport.html
Hazelnuts are far more common than peanuts; in fact peanuts are still considered mostly a savoury item and are still somewhat rare in sweets such as chocolate bars. Hazelnuts are almost the equivalent to peanuts in America ie you would find those much more commonly in sweet foods.
If you are flying, the Anapen site has a form you can fill out for use at the airport. It may never be requested, but it is good to have on hand.
http://www.anapen.de/AttestFlughafen.pdf Since it is an explanation in both German and English, it can also be helpful if you do need emergency services. I know from first hand experience that stress of a medical emergency can make one forget key vocabulary items; this happened to me in France awhile back even though I am very comfortable with the language.
For France, I would avoid baked goods, frankly. The flour contains lupine flour so if a nut allergy, this is maybe something you should avoid altogether, but you would know best.
http://chowhound.chow.com/topics/624177