Is it permissible to rinse the mouth and nose separately during wudu, and is the hadith mentioned in this regard authentic?

In ablution, rinsing the mouth and sniffing water into the nose separately is permissible, and it is also permissible to separate them. However, it is better to combine them from a single scoop of water, as this is established by authentic and stronger hadiths than those that indicate separation. Although some hadiths suggest separation, they are weak and not established, such as the hadith (definition) of Talhah ibn Musarrif. There is a difference of opinion among the schools of thought: the Hanafis and Malikis believe in separation, while the Shafi'is and Hanbalis believe in combining them. This is a matter of ijtihad (definition) (independent reasoning), so both methods are valid and fulfill the essence of the Sunnah (definition). The disagreement is only concerning which method is superior.