The information that Woodside was killed in the 13 March 1862 action at Spring River, Arkansas near the Missouri border came from the report of the Union troop commander, Lieutenant Colonel Samuel N. Wood of the 6th Missouri Cavalry. This you can read in the "War of the Rebellion Official Records of the Union and Confederate Armies," series 1, vol. 8 (of 128 volumes), p. 338. In LTC Wood's report he wrote "Prisoners taken report among the dead Colonel Woodside." Take it up with him. I am unable to help you with the other information you requested, but perhaps someone else can.
Bruce Nichols