Damage dealt to you causes you to lose that much life.

First Response looks at the entire previous turn to determine whether its ability triggers or not. It doesn't matter whether First Response was on the battlefield when you lost life.

First Response checks only if you lost life during the turn, not whether your life total decreased over the course of the turn. For example, if you lost 2 life and then gained 8 life last turn, First Response's ability will trigger.

Only one Soldier will be created no matter how much life was lost.

The Soldier won't be able to attack the turn it's created (unless something gives it haste).