Eliezer,
1. The Shulchan Aruch (OC 8:2) only says that it is “correct”. That it is to say, it is a good custom to be yotzi all opinions (Aruch haShulchan seif 6) . The Mishna Berura (s”k 4 says that someone who was never married should not.
2. The SA says until chatzot. The Rema says that after chatzot it is prohibited. The Mishna Berura (s”k 7) brings the opinion you cited and rejects it with both hands. Even one second after chatzxot is too late. The Aruch haShulchan (seif 14) also says that after chatzot one may not daven Shacharit. Rather one should first daven Mincha and then daven tashlumim.