To the best of my knowledge, when you loot gear, one of the mods (armoring, I believe) is not removable. You can customize your gear to a point, swapping the other mods in and out as you see fit. If you want to fully customize the item, you need gear that has nothing in the Armoring slot to start with (which is why crafting produces unslotted items now)
This is true with Sabers, Blasters, and Armor.
This is incorrect.
The only class of item you cannot remove the Armoring from is Purple Artifact gear from Endgame Operations (and PvP?).
At every other level you can.