Yes, it was pretty common to have feuds and other small disputes solved by small-scale warfare in medieval Europe, particularly in the early and central Middle ages (it trails off at different points in different parts of Europe, but it's pretty common everywhere until at least c. 1150, if not later). How common it was depended very much on how powerful the king was and how much he cared about the conflict - if he decided it was worth the political capital to stamp it out, he probably could have in most situations. Another thing to remember if that, of course, the king himself (or the royal family, particularly adult sons/brothers of the king) were very often involved in squabbles like this. There wasn't really any discernible difference between the German Empire and the rest of Europe in this regard - local squabbles are just as prevalent, although due to the sheer size of his territory, as well as his frequent trips to Italy, it's notable that the Emperor/King tends to be less frequently involved in Germany than in, say, France (although this could well be a reflection of our surviving sources and the historiography of both countries rather than a sure fire fact.

If you want more information on how these kinds of squabbles worked themselves out, I've written on them before here.

One final point. It most likely wouldn't have been levies (that is, part-time peasant soldiers) who would have fought in these conflicts. Instead, it would have been small, well-trained groups of aristocratic knights and retainers which would have done the majority of the fighting.