Assalaamu alaykum wa rahmatullaahi wa barakaatuh, Shaykhs. The Hanafis give the following hadiths as evidence regarding the Witr prayer and that one is to say the Takbeer (saying: Allahu Akbar) and raise his hands like one does when he starts a prayer and then recite the Qunoot supplication:
1) Ibn Abi Shaybah narrated in his Musannaf (no. 7021) from Al-Aswad that ‘Abd Allah ibn Mas‘ood when he completed the recitation in the third unit of prayer of the Witr, would say Takbeer and then recite the Qunoot, and when he completed the Qunoot, he would say the Takbeer and bow.
2) Ibn Abi Shaybah narrates in his Musannaf (no. 7027, 7028) that ‘Abd Allah ibn Mas‘ood would raise his hands when reciting the Qunoot.
3) Abu Haneefah reported from Hammad (ibn Abi Sulayman) from Ibrahim (An-Nakhaa‘i) that the Qunoot is obligatory in the Witr within Ramadan and outside of it before bowing, and when you wish to recite the Qunoot, say Takbeer, and when you wish to bow, say Takbeer also. (Kitaab Al-Hujjah, 1:200)
There are many hadiths, I could not provide all of them due to the limitation on the amount of words. They say that these are not weak hadiths. Moreover, they say that one is to sit after two units of prayer and then recite Tashhahud and then rise for the third unit of prayer. They give the following as proof: “When you sit in every two units of prayer, then say 'Attahiyyaatu lillaahi wassalawaatu wattayyibaat…'” (Musnad Ahmad, no. 4160)
The editors of Musnad Ahmad said, “Its chain is authentic according to the criterion of Muslim.” (Musnad Ahmad, 7:227)
My question is: are all these hadiths authentic, and if not, then can you provide me with details explaining why are they weak, very weak, or fabricated? I used to pray the Witr like the Hanafis say before, but now I follow the following method: Praying two units of prayer, then say Tasleem (saying: Assalaamu alaykum), and then pray one unit of prayer and recite the Qunoot after bowing in that one unit of prayer. Please take your time and provide me with authentic evidence. Please do not just give any links to similar or related questions. May Allah reward you.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.

This is one of the issues regarding which the scholars hold a famous difference of opinion. The lay-Muslim is required to follow the opinion of the scholar whose knowledge and piety he trusts. You are now following the opinion of the Shaafiʻis and Hanbalis, which is closer to the Sunnah; the Prophet, sallallaahu ʻalayhi wa sallam, said, “Prayer during the night is in pairs (of units of prayer), and if one of you fears that the morning is near, he should pray one unit of prayer of Witr, which will make what he has prayed an odd number.” [Al-Bukhaari]

It is also permissible to perform the Witr as a three-Rakʻah (unit of prayer) prayer; the Prophet, sallallaahu ʻalayhi wa sallam, said, “...and whoever wishes to perform the Witr as three units of prayer may do so.” [Abu Daawood and others] The Sunnah in this regard is to not sit for Tashahhud in the second unit of prayer due to the forbiddance of imitating the Maghrib prayer. Al-Haafith Ibn Hajar said:

“To reconcile between this hadeeth and the previously cited hadeeth that forbids imitating the Maghrib prayer is that it is forbidden to pray a three-Rak‘ah Witr with two Tashahhuds (in the second and third units of prayer), and this was also practiced by the righteous predecessors. It was narrated on the authority of Muhammad ibn Nasr from Al-Hasan that ʻUmar used to rise for the third Rakʻah of the Witr with Takbeer. It was also reported from Al-Miswar ibn Makhramah that ʻUmar performed the Witr as three Rak‘ahs with one Tasleem at the end of the third Rakʻah. It was narrated from Taawus from his father that he (ʻUmar) used to perform the Witr as three Rak‘ahs without sitting between the second and third Rak‘ahs. The same was narrated from Qays ibn Saʻd from ʻAtaa' and Hammaad ibn Zayd from Ayyoob. Muhammad ibn Nasr narrated from Ibn Masʻood, Anas, and Abu Al-ʻAaliyah that they prayed the Witr as three Rak‘ahs like the Maghrib prayer; it is as if the mentioned forbiddance in this regard had not reached them. We shall address the statement of Al-Qaasim ibn Muhammad about the permissibility to perform the Witr prayer as three Rak‘ahs; however, the difference of opinion in this regard is in making this (praying Witr as three Rak‘ahs) obligatory, as this is not supported by the authentic ahaadeeth.”

As for the Qunoot supplication, it is an easy, flexible matter. It is permissible to recite the Qunoot before bowing according to what you mentioned of the reported practice of the Companions. It is also permissible to recite it after bowing, and this is better because it has been authentically reported from the Prophet, sallallaahu ʻalayhi wa sallam.

Ar-Rawdh combined with its Haashiyah reads:

“And he recites the Qunoot in the third Rak‘ah after bowing as a recommended Sunnah, because it was authentically narrated that the Prophet, sallallaahu ʻalayhi wa sallam, used to do that, as narrated on the authority of Abu Hurayrah, Anas, and Ibn ʻAbbaas except that this (the Qunoot after bowing) was relevant to the obligatory prayer. It was authentically reported with regards to the Witr on the authority of ʻUmar and ʻAli. It was also narrated that the rightly-guided Caliphs and other Companions used to recite the Qunoot after bowing. Al-Khateeb said that this was the practice of most of the Companions. If the Qunoot is recited before bowing, after reciting the Quran, this is also permissible. Abu Daawood narrated on the authority of Ubay ibn Kaʻb that the Prophet, sallallaahu ʻalayhi wa sallam, used to recite the Qunoot in the Witr prayer before bowing. This practice was authentically reported from a group of the Companions. Al-Khateeb said, ‘The ahaadeeth reporting that the Qunoot is recited before bowing all have ʻIllah (hidden defects).’”

Shaykhul-Islam Ibn Taymiyyah said, “Some scholars held that the Qunoot is to be recited only before bowing, and others held that it is to be recited only after it. The jurists among the scholars of Hadeeth, like Ahmad and others, held that both practices are permissible because both were reported in the authentic Sunnah. However, they preferred reciting the Qunoot after bowing because it is mentioned more often and analogy supports it.”

In brief, the Qunoot performed in the manner described by the Hanafis was narrated on the authority of a group of the Companions, and it is authentic, as mentioned above. It is permissible, although reciting it after bowing is more preferable. The majority of the scholars held that performing the Witr as three Rak‘ahs is permissible and not obligatory, contrary to the Hanafis. The reconciliation between the relevant texts is what we have presented to you above, and the lay-Muslim is required to follow the view of the scholars which he trusts, as we mentioned.

Allah knows best.