Kruskal's and Prim's algorithm
By definition MST or Minimal spanning tree is defined on undirected graph only!

But if you are really want to (and I wander why) You can "make" Kruskal's algorithm work on it ,but you have to make sure you are ignoring loops because otherwise if you got a loop with small weight the algorithm will count it on the "MST" (because it isn't really MST).

Regarding to Prim's algorithm I can't see a way you cane make this work on directed graph.

I don't know other uses of Kruskal's and Prim's and I don't believe there are. Usually you make a slight changes on the algorithm in order to make them do something slight different.