What German product is the equivalent of cream in a recipe from the United States?
"Cream" is most certainly süße Sahne. A modifier gives you knowledge about the fat percentage. Half and half refers to 20% fat, which you could mix yourself if needed, but few recipes are that sensitive, so you can use milk (Vollmilch, 3.5) or whipping cream (Schlagsahne, 30 to 35 percent). The only problem is double cream. That's Konditorsahne, at inner 40 percent, and not available retail in Germany. If it has to be whipped, you have to find a high-ish Schlagsahne (33 instead of 30), drizzle some Sahnesteif, and cross your fingers. 

If the recipe needed a cultured product, it would have specified Greek yogurt (10) or sour cream (10 to 20, use saure Sahne or Schmand for that). Creme fraiche is not used in traditional American recipes, as it is a rare and expensive imported product. You can use it in a recipe calling for sour cream, obtaining a product with a richer mouthfeel and less tanginess. 

The "what type of cream is suitable" question is unrelated to terminology and should be asked separately. Briefly, the answer is "all of them".