It helps if the base geometry has somewhat even subdivisions, it doesn't have to be a lot but give the displacement something to work with. Corner edge loops/bevels helps keep the shape but UV seams along with hard normals also play a part in breaking up displacement. You have the choice of using displacement or subdivision approximation node, both have their place.


Left column:
corner loops
soften normals
no uv seams on corners
subdiv approx

Right column:
corner loops
hard normals
no uv seams on corners
no subdiv approx

And for the weird gaps in your second problem, it's tough to judge without looking at the scene (wrong uv set being used?).