All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
According to the Hanafi School of jurisprudence, the Witr prayer is three Rak'ahs with one Tasleem and with two Tashahhuds. They provided evidence that the Prophet used to perform the Witr prayer with three Rak'ahs; this authentic narration reads: "Then he performed the Witr prayer without any interruption between them" [Ahmad and An-Nasaa'i]. However, it does not suggest that he performed the prayer with two Tashahhuds, rather he ended the prayer with one Salaam at the end of the three Rak'ahs. There is no evidence for performing it like the Maghrib prayer with two Tashahhud. On the contrary there is evidence that it is disliked to perform the Witr prayer like the Maghrib prayer. The Prophet said: “Do not perform the Witr prayer with three Rak'ahs and make it like the Maghrib prayer.” [Al-Haakim]. Therefore, this narration is evidence that it is disliked to perform the Witr prayer like the Maghreb prayer with three Rak'ahs and with two Tashahhuds.
As regards reciting a chapter after the Al-Faatihah, in the three Rak'ahs, then there is an authentic narration about this. Ubay Ibn Ka'b narrated that the Prophet used to perform the Witr prayer three Rak'ahs, and would recite after Al-Faatihah in the first Rak'ah chapter 87, chapter 109 in the second Rak'ah, and chapter 112 in the third Rak'ah.
With regard to your question about the obligation of raising the hands while saying the Qunoot supplication, then we have not come across a statement from the Hanafi School of jurisprudence about this, rather they stated that it is only recommended.
Furthermore, there is no evidence about the Takbeer after finishing the recitation of Quran and before the Qunoot supplication. What is even more strange is that they [Hanafi School] are of the view that it is an obligation to prostrate for forgetfulness if one forgets this Takbeer.
Allaah Knows best.