They are particularly fond of peanuts and golden syrup, especially if mixed together. But they normally eat worms, and, as you so rightly say, stuff. (They are clever enough to know that you find lots of worms in cow pats of a certain age, much to the annoyance of dairy farmers). They also enjoy apples. I used to work in an orchard where, if you drove around of an evening in September, there'd be badgers lumbering off in all directions ahead of you like rabbits scattering, some with windfalls still in their mouths.
I think the similarity between Meles and mel is a co-incidence. Meles is just what ancient Italians called a badger!