Included bark can be remedied by removing the smaller of the two branches, or the one supporting less of the overall mass. However, if the diameter exceeds six inches, don't remove it. The resulting wound could do more harm to the tree than the inclusion. The tree can be saved by heading back the branch you would like to remove. These cuts will suppress the pruned branch and allow the unpruned branch to grow and become the tree's dominant leader.
Dead wood offers a prime entry point for pathogens like bacteria and fungi.
Carefully cut any dead wood away, avoiding the live portion of the tree. Leave a half inch of dead wood. If you make your cut into the living area, the tree will have to re-heal. This is the only time that leaving a stub on the tree is considered correct. Crossed branches are unhealthy.