Ward and protection exist in places other than the battlefield, right? If a creature with ward or protection is targeted in the graveyard or on the stack, they still apply, right?

No. Abilities by default only work on the battlefield unless they have to work elsewhere or they say so explicitly.

Goblin Piledriver can be targeted by Essence Scatter.

I was going to say take a look at how the changeling mechanic is worded, but it's been changed over time.
Originally it said "(This card is every creature type at all times.)", but it was [url=Bloodline Pretender]updated to[/url] just "(This card is every creature type.)"
I guess the operative part making a changeling all creature types at all times is that it says "this card".
Which has me wondering, would a card that said "this card has protection from X" have protection in other zones?

No, it's because changeling is a characteristic-defining ability. I missed that exception in my post. Characteristic-defining abilities like changeling, devoid, Tarmogoyf's, or Transguild Courier's work everywhere. These are abilities that say "This card's name, type, color, power, and/or toughness is THIS."