I have some data for you in the way of clarification. First, you are correct in what the coast artillery was...Coast Artillery units were the men who manned the heavy coastal defense guns, but only after 1901. The first Coast Artillery unit was not formed until 1901 and that was the 71st Coast Artillery (that makes sense..the first being number 71st...in a government sort of way).
Significantly, the Spanish American War ended on December 10, 1898. The Coast Artillery was not formed until 1901 (see http://www.spanamwar.com/coastartillery.htm)http://www.spanamwar.com/coastartillery.htm). Maybe he served in the 3rd U.S. Artillery before joining the Coast Artillery? Technically, he could not have been a Spanish American War vet but maybe a vet of the Philippine American War (in some instances, like pension records, it is a moot point. The government grouped them together back then for pension funding reasons, though now the two wars are recognized by all, including the government, as being seperate conflicts).
Anyhow, for the pension records request, the basic info needed to apply is name; branch of military - army in this case; time period or war - Spanish American War/Philippine American War in this case; and state he was from...perhaps you know that.
The other questions help them narrow the search but are not part of the required minimum info.