Ibn Majah

Commentary:
(1)
From this hadith, it is understood that merely putting water into the nose is not sufficient; rather, if needed, the nose should be thoroughly cleaned.

(2)
For istinja (cleansing after relieving oneself), it is necessary to use three stones (or similar materials).
If there is a need to use more than three stones, it is permissible to do so; however, their number should be odd.
And Allah knows best.

43. Commentary: The argument that this hadith proves the sufficiency of one stone is weak, because there is no explicit mention of one stone here. The Imam’s reasoning is based on the word “odd” (ṭāq), which, according to him, includes even the number one. However, in other hadiths, the use of less than three is explicitly negated, as in the previous hadith (41) and in Sahih Muslim, where it is narrated from Salman radi Allahu anhu that the Messenger of Allah sallallahu alayhi wa sallam forbade us from performing istinja (purification after relieving oneself) with less than three stones. [صحیح مسلم ، الطھارۃ ، حدیث : 262]

No single hadith can be separated from another hadith. By reconciling the narrations, it becomes clear that the “odd” (ṭāq) mentioned here refers to three or any odd number above three, because the principle is that an absolute (mutlaq) evidence is interpreted in light of a restricted (muqayyad) one. And that is: the hadiths permit sufficing with at least three stones, not less than that, because doing so is religiously prohibited. However, in a situation of necessity—when three stones cannot be found—then it is permissible to use two or even one stone, or to use one stone three times, because normal circumstances cannot be interpreted in light of exceptional situations. And Allah knows best.

1:
Because according to them, both of these acts—ablution (wudu) and ritual bath (ghusl)—are obligatory (fard) in both cases.
Their evidence is precisely this hadith,
in which the imperative form (sighah al-amr) is used,
and the imperative form indicates obligation (wujub),
unless there is some contextual indicator (qarinah) present by which the imperative form is shifted from the meaning of command and obligation to the meaning of recommendation (istihbab), which, according to them, is not present here.
The author of Tuhfat al-Ahwadhi is also a supporter of this view.

2:
According to these people, both of these acts are Sunnah (masnun) in ablution (wudu) and obligatory (wajib) in the state of major ritual impurity (janabah), because in janabah there is a command for thorough purification.

3:
This is the view of the majority of scholars (jumhur al-‘ulama), because apart from ‘Ata’, it is not transmitted from any Companion (sahabi) or Successor (tabi‘i) that they held the view that prayer performed without rinsing the mouth (madmadah) and nose (istinshaq) should be repeated.
Thus, this act is Sunnah, not obligatory (fard) or necessary (wajib).

Benefit:
The inference that one lump (stone) is sufficient from this hadith is weak because there is no explicit mention of one lump here. To deduce from the word "odd" (ṭāq) that it includes one, whereas in other ahadith there is explicit negation of less than three, as in Sahih Muslim where it is narrated from Sayyiduna Salman (radi Allahu anhu) that the Messenger of Allah (sallallahu alayhi wa sallam) forbade us from performing istinja (purification after relieving oneself) with less than three lumps. [صحيح مسلم : 262]

One hadith cannot be separated from another hadith. By combining the narrations, it becomes clear that here "odd" refers to three or an odd number above three, because the principle is that an absolute evidence is interpreted in light of a restricted one, and that is: in the ahadith, permission is given to suffice with at least three stones. Not less than this, because doing so is religiously prohibited. However, in a situation of necessity, when three lumps are not available, it is permissible to use two or one lump, or to use one lump three times. Therefore, general circumstances cannot be interpreted in light of situations of necessity. And Allah knows best. [سنن نسائي متر جم دارالسلام : 1 /117]