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Protection protects you from being:
You are NOT protected from spells that do not specifically target a creature/player. For example, a creature with protection from white would still be destroyed by Wrath of God (it doesn't TARGET the creature; it deals no DAMAGE to the creature), and a creature with protection from black would still be sacrificed by Diabolic Edict if the player chose to sacrifice it (spell targets the PLAYER, not the creature).
Planeswalkers uniqueness is confined to each player. That means Player 1 can have Jace Beleren and Player 2 can have Jace, the Mind Sculptor in play at the same time. If a single player plays two Planeswalkers of the same subtype, that player chooses which one to put into the graveyard.
Damage that would reduce the life of a player can be redirected to that player's planeswalker instead.
Legendary uniqueness is confined to each player. That means Player 1 and Player 2 can both have Avacyn, Angel of Hope in play at the same time. As soon as a player gains control of another one (whether though cloning, mind controlling, or creating a token copy), that player chooses one to put into the graveyard.
When deciding who has priority, follow the APNAP rule: Active Player, Non-Active Player
Spells get placed on the stack and resolve in reverse order and the timing can change the outcome of battle. A contrived example: