ANSWER:

You can do all of that as the time of tahajjud is a blessed time and making duaa was not for the sake of it being after the prayer but rather due to the time of tahajjud and the last third of the night.

QUESTION: Sheikh, in the case of Tahajjud prayer, the dua is long indeed. So should we ask Allah whatever we want in sujood and last tasahhud ? Or we can make dua after prayer with hands up (which is not recommended in general salah)?