The amount of life gained is equal to the sacrificed creature's toughness as it last existed on the battlefield.

If the target creature is an illegal target by the time Severed Strands tries to resolve, the spell doesn't resolve. You don't gain life.

If the target creature is a legal target but can't be destroyed, most likely because it has indestructible, you still gain life.

You must sacrifice exactly one creature to cast this spell; you can't cast it without sacrificing a creature, and you can't sacrifice additional creatures.