Yes, fire protection stacks. To test this, I put on a diamond helmet with Fire Protection I and stood in fire. Then, I put on an entire suit of diamond armor with Fire Protection I and went to stand in the fire again. I took no damage, though my armor took extensive damage.
This is the video I made in the process (I'm not sure I've properly annotated it, but hopefully you can tell what I'm doing. :P):
Protection will stack on different armor pieces, and provides comprehensive protection against all forms of damage except The Void and server kill commands. It is true that falling, fire, lava, poison, and even mob damage will be reduced, but false that the armor durability will always reduce more than normal. When falling off a building with Protection IV boots, the boots will not suffer any damage, producing the same results as feather falling III boots. The Armor will take more damage from Mobs and Players however.
It is possible to get feather falling IV AND protection IV boots, reducing fall damage immensely. All other pieces of armor with protection will add additional damage reduction in the same way the boots would. Protection appears to be one step down from specific defenses (ex: Protection III = Feather Falling II when taking fall damage, or Protection III = Fire Protection II when in lava).
TL;DR- Protection enchantments are slightly less effective than specific ones, but protect against everything at once. The best possible armor would be:
Helmet: Respiration III, Aqua Affinity I, Protection IV, Thorns III
Chest and legs: Protection IV, Thorns III
Boots: Protection IV, Feather Falling IV, Thorns III
Note that Only highest Level of Thorns take effect if present on multiple peices of armor. Source
Best Answer
You cannot get two Protection enchantments on one item with vanilla enchantment or using books. You can do this using the
/give
or/summon
command though (this command will give the nearest player iron leggings with Protection III and Feather Falling I):Look at another answer to get more information how the command works.
The enchantment IDs can be found on the Minecraft Wiki.