I'm want to install a stockade fence in my backyard. I have a tree behind in the corner. Should I just attach the fences to the tree or install another post.

I would suggest installing another post. At least then, you will know for sure how secure the attachment to the post is.

Also nailing into a tree can damage it and cause it to die. :(

Yes it will cause damage and can also be disfiguring to the tree. A tree could die. But, how it is done that makes the difference. Please remember that arborists often cause larger wounds injecting iron or other mineral nutrients into trees in order to help the trees.

You will want to install another post, the tree will grow and pull the fence upward as it does. But place the post clear of the roots as much as possible