Garrus

Garrus's Tier III Alt red says: "Target a unit adjacent to you. After the attack: You may move up to 2 spaces to a space adjacent to an enemy hero; if you do, push that hero 3 spaces, ignoring obstacles." Does the "after the attack" part target an enemy hero before or after movement? Can you move to a space adjacent only to an immune enemy hero? The wording here is similar to Cutter's Primary Green.

You cannot. Check page 10.

Can you discard a card to defend even if you don't have enough defense value to survive the attack?

Yes, you can discard and die.