Oak tree question
The white fuzzy-looking growths on the dead limb appears to be lichens. Lichens are two-part organisms that are self-sufficient and harmless to their hosts. See the link below.
If not lichens, these growths could be a decay-causing fungus that breaks down dead wood, similar to the fungi that grow on a dead log on the forest floor. Again, nothing to be concerned about, just Mother Nature's normal activity.
Is you second picture showing the inside of the same dead limb? Oak wilt does produce a a distinctive fruiting body, called a spore mat, which is black and have an elliptical shape; however, these are present on the outside of the tree usually on the trunk or large branch. It is still possible that your tree is dying from oak wilt; however, I cannot make a positive diagnosis from your photographs.
If this is a valuable tree to you, I recommend you contact local tree services; ask them if they have a certified arborist on staff; and if so, have him or her come to your landscape and examine your tree. An arborist will be able to tell you what is going on with your tree and whether or not it can be saved.
The links below will give you valuable information regarding oak wilt: