1. Was Paddy's Lamentation written during the American Civil War?
A line reads, "There is nothing here but war," present tense. So the war is a current thing, per the song's narrator. Of course, there are a number of songs written after an event that speak of it in the present tense. I would be interested in knowing when the words first appeared in print (the 1864 "Paddy's Lament" being an entirely different song)
2. What was meant by the term "Indian Buck"?
a. "Indian buckwheat" is mentioned in 1866: "All About Buckwheat... Varieties of Buckwheat... A variety called Indian buckwheat (P. Tartaricum) is grown to some extent in New England, for fattening swine, not producing flour palatable as human food. The kernel is harsh, coarse and nearly ovate." July 11, 1866 [Butler, Pennsylvania] American Citizen p. 4, col. 1, available on the LOC's Chronicling America website.
b. However, there is no evidence that Indian buckwheat was ever exported to Ireland; whereas, by contrast, the export of Indian corn (both in the shell and milled into cornmeal) to Ireland during the Famine is well documented. See Cecil Woodham-Smith, The Great Hunger (London: Hamish Hamilton 1987).
c. Consequently, I think it likely the song in question refers to Indian corn, not Indian buckwheat.
d. So why did the songwriter not say Indian corn? Because it wouldn't rhyme.