“Half-fiend” is an inherited template that can be added to any living, corporeal creature with an Intelligence score of 4 or more and nongood alignment (referred to hereafter as the base creature).
“Fiendish” is an inherited template that can be added to any corporeal aberration, animal, dragon, fey, giant, humanoid, magical beast, monstrous humanoid, ooze, plant, or vermin of nongood alignment (referred to
hereafter as the base creature).
“Vampire” is an acquired template that can be added to any humanoid or monstrous humanoid creature (referred to hereafter as the base creature).
So no to Fiendish, no to Vampire, but as long as you consider an elemental living (I believe non-living only applies to constructs and undead, so they should be fine there), you can have a Half-Fiend Elemental.
Generally, any template will tell you what it can apply to.
-Hyp.