Why am I having unusual issues with shadows not casting correctly?

As Roel has suggested improving the lightmap resolution can help along with good UVs.

  • The image with the window and the diagonal lines looks directly related to UVs. Can you post an image of the UVs for this?

With the mesh with the white line make sure that the meshes are overlapping a little bit as this will help alleviate any light bleed like this you are seeing.