Boot the tire with a dollar or park tool but definitely replace it when you have the chance.
Don't do this. The tire is fine. It was a nail puncture, not a gaping sidewall.
Ride the tire, forget about it. Sure, it will be weaker, if you happen to hit another nail at the EXACT same spot that this one hit.
Check out those RhinoDillo tire liners that were posted above me. They work.