1. The card says that after defending the attack, you may move 1 or stand up. Does this imply that the card knocks you down (so you either end up prone 1 space away or standing in the same space), or is the "stand up" only relevant if you were bitten while prone? Can you move 1 even if you were prone when you moved the card?
It's the or that matters there. After defending the attack, you may either stand up in place if you were already knocked down, or you may move 1 space. You don't end up prone, and you can't move while you're prone so that's why you can choose. As a reminder, it's a MOVE so it does trigger extra attacks if you move adjacent to another zombie.
The card is useful if you've been knocked down because it defends, and you then make zombies roll rather than "Well, looks like I'm going to die."
2a. If you play the card to defend against the first attack triggered by moving into a space, and move 1 as a result of the card, what happens to other attacks triggered by the original move. Are they ignored?
2b. I'm assuming the "move 1" would trigger additional attacks in the space moved to since it's not a "rush"?
That is correct. If you move into a space, it triggers an attack. If you rush or are pushed into a space it does not.
3. I'm assuming you can't "move 1" onto an obstacle? There's another card that allows rushing 1, but specifically states that obstacles are ignored during the action.
That's correct. You need 2 movement/stamina in order to get onto an obstacle.