Emma's traumatic flashback of the dying commander was based on both historical fact and legend https://www.battlefields.org/learn/biographies/hugh-mercer.
https://www.revolutionary-war.net/general-hugh-mercer/
The oak tree was real and stood in Princeton battlefield for centuries until it died. Now if you go, you'll see a young oak tree that is the descendant of the original tree and is growing strong!
*not my picture but I have seen the original and legacy tree (shown here.)