The ahadaith mentioned/ referred to in the video. Video courtesy of Hanafi Fiqh Youtube Channel.
Prophet Muhammad (SAW) said, “There is no wudu for him who does not mention Allah’s name upon it.” (Sahih – Ibn Maajah, At-Tirmithee, Abu Dawood, and others)
Humran (RA) narrates that Uthman (RA) called for water to make wudu and washed his hands three times… then said, “I saw Rasoolullah (SAW) make wudu just as I have made wudu.” (Sahih – Al-Bukhari and Muslim)
Prophet Muhammad (SAW) said, “When you make wudu then wash your mouth.” (Sahih – Al-Baihaqee)
The Prophet (SAW) said, “When one of you makes wudu then let him enter water into his nose, then expel it.” (Sahih – Al-Bukhari, Muslim, Abu Dawood)
Abd Khair (RA) said, “We were sitting looking towards Ali (RA) – as he made Wudu – and he entered into his mouth a handful of water with his right hand and washed his mouth and nose, then expelled it from his nose with his left hand – he did that three times, then said, ‘Whoever would like to see the way of purification of Rasoolullah (SAW) – then this is his purification.'” (Sahih – Ad-Daarimee)
Allah (SWT) said, “O you who believe! When you intend to offer prayer, wash your faces and your hands (fore-arms) up to the elbows, rub (by passing wet hands over) your heads, and (wash) your feet up to ankles…” (Al-Ma’idah 5:6)
Humran ibn Abaan (RA) narrates that Uthman (RA) called for water to make wudu and so mentioned the way in which the Prophet (SAW) made wudu. Humran (RA) said, “Then he washed his face three times.” (Sahih – Al-Bukhari, Muslim)
Anas (RA) narrates that the Prophet (SAW), when he made wudu, used to take a handful of water and enter it below his chin and rub it through his beard and said, “This is what my Lord – the Great and Exalted – has ordered me to do.” (Sahih – Abu Dawood, Al-Baihaqee, Al-Haakim)
Allah (SWT) said, “O you who believe! When you intend to offer prayer, wash your faces and your hands (fore-arms) up to the elbows, rub (by passing wet hands over) your heads, and (wash) your feet up to ankles…” (Al-Ma’idah 5:6)
Nu’aim ibn Mijmar (RA) said, “I saw Abu Hurairah make wudu – he washed his face and completed the wudu, then washed his right hand until he reached the upper arm, then his left hand till he reached the upper arm” – then in the end of the Hadith he said: “This is how I saw Rasoolullah (SAW) make wudu.'” (Sahih – Muslim)
Allah (SWT) said, “O you who believe! When you intend to offer prayer, wash your faces and your hands (fore-arms) up to the elbows, rub (by passing wet hands over) your heads, and (wash) your feet up to ankles…” (Al-Ma’idah 5:6)
Prophet Muhammad (SAW) said, “The two ears are a part of the head.” (Sahih – At-Tirmithee, Abu Dawood, and Ibn Maajah)
From Abdullah ibn Amr (RA) – about the way of performing wudu – he (SAW) said, “Then he (SAW) wiped his head and entered his two forefingers into his ears and wiped the backs of his ears with his thumbs”. (Sahih – Abu Dawood, An-Nasaa’ee, Ibn Maajah, Ibn Khuzaimah)
Ar-Rabee bint Mu’awwidh (RA) reported that the Prophet (SAW), “Wiped his head with water remaining in his hand”. (Hasan – Abu Dawood and others)
Allah (SWT) said, “O you who believe! When you intend to offer prayer, wash your faces and your hands (fore-arms) up to the elbows, rub (by passing wet hands over) your heads, and (wash) your feet up to ankles…” (Al-Ma’idah 5:6)
“Ibn Umar (RA) said, “Rasoolullah (SAW) fell behind us and then came upon us during a journey, then we found him and it was time for ‘Asr – so we began to make Wudu and wipe over our feet, so he (SAW) called out at the top of his voice, ‘Woe to the ankles from the Fire. (two or three times)'” (Sahih – Al-Bukhari and Muslim)
“Al-Mustaurad (RA) said, “When the Prophet (SAW) made wudu he would enter the water between his toes with his little finger.” (Sahih – Abu Dawood, At-Tirmithee, and Ibn Maajah)
Rasoolullah (SAW) said, “None of you makes wudu and completes the wudu then says: “Ash hadu an la ilaha illal lahu wah dahu la shareeka lahu wa ash hadu an-na muhammadan ‘abduhu wa rasulhu” except that all eight Gates of Paradise are opened for him – so that he enters by whichever he pleases.” (Sahih – Muslim, Abu Dawood, At-Tirmithee, An-Nasaa’ee, Ibn Maajah)
“Allah hum maj ‘alnee minat taw-wabeena, waj ‘alnee minal muta tah-hireen.” (Sahih – At-Tirmithee)