Rin y Seri, inseparables

An ability that triggers when a player casts a spell resolves before the spell that caused it to trigger. It resolves even if that spell is countered.

If the chosen target is an illegal target by the time Rin and Seri's last ability tries to resolve, the ability won't resolve. You won't gain life.

Rin and Seri's first two abilities don't trigger when you cast Rin and Seri.

The amount of damage Rin and Seri's last ability deals is determined only as that ability resolves. If Rin and Seri is still on the battlefield, it'll count itself.