Nazir 15: To Contradict a Mishnah

A new mishnah: on a compound vow of becoming a nazir when a son is born to him, and also for 100 days. How do those two elements of the vow work together, overlap, preempt, or delay each other? Also, how Rav expresses his contradiction of the mishnah. How does the timing line up with haircutting and mourning, in that event. Plus, the comparison to the count of Hilkhot Niddah, the laws of family purity, which also has a count and a requirement of being able to become pure.