My boyfriend and I (we're both native speakers of English) talk about making food all the time. There's nothing weird about making chicken, making rice, making soup, making fish, making pasta, etc.
"Cooking" and "preparing" (when "preparing" is used with food) are more specific culinary terms. "Cooking" usually involves heating the food, while "preparing" does not. You can "prepare" a food item without actually "cooking" it, as is the case with a salad. "Preparing" is often a step before "cooking". For example, "preparing the chicken" can mean adding seasoning and spices to it before heating it up in the oven. "Making" is used in a pretty general, broad sense when used with food items (though sometimes "cooking" is used in this sense as well - depends on the speaker). When my boyfriend says to me, "I'm making chicken tonight", he means that he's going to do the preparing and cooking of the chicken (and most importantly, it means that I don't have to make dinner! :-D)
Here the translation in french is easier and more natural than in english. on "fait du café". In english we do not "do coffee", we make coffee. litterally it would be fabriquer or créer. The problem is we came to a point where the difficulty is no longer to translate from danish but translate to english. Fabriquer du café ?!??!? The danish sentence is very easy to understand and the english translation means the guy is cosplaying a pullet