Should I be saving the essence of fate that I get for later in the game for some reason like saving Dragon Bones in Skyrim to maker the Dragon Bone armour or should I just turn it into Fate potions whenever I get it?
Essence of Fate do have greater usage than purely the Fate Potions - when you reach level 5 alchemy, adding an Essence of Fate into the recipe of what would have made a 'greater' tier potion, would instead result in a 'master' tier potion being made.
I.e. 3 Black Cohash + 2 Embereyes + 1 Bloodroot = Greater Health Potion 3 Black Cohash + 2 Embereyes + 1 Bloodroot + 1 Essence of Fate = Master Health Potion
Aside from Alchemy however, Essence of Fate don't have any further usage, so no, there's no need to be saving them up