"He dies in December."
Translation:Muore a dicembre.
Maybe mention "presento storico" as an explanation in the question so you don't seem like a Mafia thug? (That was mentioned a few questions ago in the comment section. Apparently it would be used, for example, if I was telling you, "Romeo and Juliet fall in love. They plan to run away together, but they die in December." I hope I'm using it correctly. Sorry if it doesn't make much sense.)
'dicembri' is the plural of 'dicembre' so you would use it in place of 'decembers'. Nouns ending in 'i' are almost always plurals (there may be a few exceptions).
If a noun ends in 'e' it could be a plural (usually of a singular ending in 'a'), or singular, which is probably at the heart of your confusion.
WordReference is a good place to check a word's plurality, for example on page: http://www.wordreference.com/iten/dicembre
The line "Forme flesse di 'dicembre' (n): pl: dicembri" shows the spelling of both the singular and plural.
Because it's "dies", not "is dead". And if that were the case, it would be "Lui è morto" or "Lei è morta".