Yes. If his post-procedure semen analysis negative, then there is no need for additional contraception. While not 100% effective (the "act of god" pregnancy can still occur), if negative then there should be no worries.
Very reliable. If a vasectomy is performed correctly, there is no need for additional contraception because it is >99% effective.
He can go to his regular doctor for a semen analysis. If no viable sperm are seen on a sample, then you should not require additional contraception.