That poem was written by Willie Lincoln (Abe's son) upon hearing of the death of family friend Col./Sen. Edward D. Baker at Balls Bluff. It was printed by the editor of the Washington National Republican, though I could never find that man's name. (Editors always get the shaft. . . .) He is on record as saying it was a "quite creditable" first attempt at poetry.
William W. Lincoln (Willie), Col. Edward D. Baker killed at Ball's Bluff. Willie or his father sent the poem to the National Republican in Washington City where both the letter and poem was published on Oct. 20, 1861. The poem was probably started by Willie and finished by his father, although it is attributed to Willie.
1. The poem was written by Abraham Lincoln's son Willie.
2. It was about the death of Senator/Colonel Edward Baker at the Battle of Ball's Bluff.
3. I think the third part of the question meant to ask "Who put it in the newspaper?" On the basis of that assumption, my answer is the editor of the Washington National Republican newspaper.
Note to players who submit questions - when your question appears in the game, please take a moment to proofread it and make sure there are no typos or missing words. If you decide a correction is needed, please send a private conversation to me and I will edit the question as soon as I can.
Great story @JOHN42768 Thanks for helping us learn about it.
William Wallace Lincoln (Willie) he would have been 10 years old, almost 11, at the time he wrote the poem. Col. Edward D. Baker - The poem was entitled "On the death of Colonel Edward Baker" wiki/Edward_Dickinson_Baker The National Republican - Willie sent the poem in to the newspaper and The National Republican published it on the front page of the November 04, 1861 issue. https://chroniclingamerica.loc.gov/lccn/sn82014760/1861-11-04/ed-1/seq-1/
Answer: Willie Lincoln about Colonel Edward Baker. In the " Washington National Republican" by Laurs Redden
Source: "Fighting in the Shadows" by Harry Lang
Edit - There doesn't seem to be a clear consensus as to the identity of the editor who approved Willie's poem to appear in the newspaper. I can't find anything on the Internet about anybody named Laurs Redden. Maybe the indicated book says that Mr. Redden was responsible for Willie's poem appearing in the National Republican, but I don't have a copy of the book, so I can't verify that.
I am giving credit for all answers that mentioned the National Republican, regardless of the name of the editor.