Is the statement that rinsing the mouth, sniffing water into the nose, and expelling water from the nose should be done three times for each mouthful and each sniff based on a prophetic hadith? And is expelling water from the nose three times after waking up a Sunnah or an obligation?

The ablution (wudu') of the one performing it is valid whether he separates the rinsing of the mouth (madmadah) and the sniffing of water into the nose (istinshaq) by using three separate scoops of water for each, or combines them using three scoops of water. The jurists differed on what is superior. The Hanafis and Malikis hold that it is better to separate them, using three scoops of water for each. Whereas the Shafi'is and Hanbalis hold that it is better to combine them using a single scoop of water. However, they all agreed on the permissibility of separating them.