ANSWER: 

You should not do qunoot in tahajjud prayer, rather you should do it in Witr. You can pray to Allah as much as you want in your sujood, both in tahajjud prayer(this is the best) as well as any other prayers. Kindly refer to the following link(s):

Is it permissible to do qunut in tahajjud prayers? I want to ask Allah to help in my educational dilemma as I’m without a university for 6 months. Is it permissible? And when does tahajjud end? At the call of adhan?

Prayer | December 21, 2017 4:07 pm
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The question is about my father. When ever he is at home he doesn’t like praying at mosque. Infact he always merge Zuhr and asr prayer togather.Alwyas.Even magrib and ishai if he is at home he doesn’t go out to pray. But he does them at home. I have been meaning to advice him by using anonymous SIM card to send him text message to advice. In fact he plays with ibadah.
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i know someone who doesn’t pray at all. not even juma’a. but in ramadan he fast but still in ramadan he doesn’t pray. that means he fasts without praying at all. does it mean that he is a kafir? and shall i consider him and call him a kafir?