Can I save this broken branch?

My neighbor was cutting trees down in their yard recklessly. One of them fell into my yard and snapped a branch of my oak tree.

What is the best way to preserve the health of the tree?

The options I see are:
1) cut it at the blue mark, 2) cut the branch off at the trunk, or 3) leave it as is.

Also, unrelated to the branch damage, I found brittle bark at the base of the tree. It broke away easily and underneath I found this dark brown wood that crumbled away easily. Is this normal for an oak, or is it a sign of an issue?

Thanks for any help!