First strike adds a damage step. If any attacking or blocking creature has or when combat damage begins, those creatures deal their damage first, in a step of their own. Then every other creature deals damage in the regular step. A creature killed in the first step misses the regular step.
Double strike deals damage in both steps, once with the first strikers and again with everyone else.
Damage stays on a creature until the end of the turn, so a hit in the first step still counts in the regular step.
Next, you choose which attacker Dwalin blocks. Its first strike saves it only when its first hit is lethal.

