I have not seen any of these things. Most of my searches up to now have been to learn ANYTHING about my grandfather's military service (if indeed he did serve), more to satisfy a nagging disconnect my late father had to his own dad, which I have now adopted. His name doesn't show up anywhere, though I have not been to the National Archives yet. These old family letters and the picture are quite a mystery.
However, what you have provided to this newcomer is like a treasure chest for me to begin digging into. My grandfather's name does not appear in the 47th Regiment roster, but the uniform information seems right on. In the past, I found this entry on a NY State Spanish American War site:
"The 47th Infantry Regiment was one of twelve New York State National Guard infantry regiments that were federalized for service in the Spanish-American War. The 47th Regiment was organized on May 27th, 1862 for a three-month tour of duty. It was recruited entirely in New York City and served in the garrison of Washington D.C. during the Civil War. The regiment also served in the draft riots of 1863, the railroad riots of 1877, the quarantine riot on Fire Island of 1892, and the switchman’s strike in Buffalo of 1895. The unit was mustered into service as the “47th Regiment Infantry, New York Vols.” at Camp Black, NY on May 24th, 1898."
And the attached photograph from "Survey of U.S. Army Uniforms, Weapons and Accoutrements" by David Cole, of this "Infantry Dress Coat with white branch color adopted in 1883" which looks very similar as well. Again, as a complete newcomer I end up taking wrong turns on my journey to figure this out. Thanks so much for your help.