There is nothing wrong with the person who prays Witr in the first part of the night or the middle of the night offering any Nafl (supererogatory) prayers he wants after Witr even though it is recommended for the last of his prayer at night to be Witr.

The time of Duha prayer is from the time when the sun has risen to a certain height, until just before the time for Zhuhr prayer.

Al-qunut should come after the ruku` but if a person recites it before the ruku` that is OK. You should raise your hands to chest level and not raise them very much, and you should spread your palms (with hands together) and hold them facing up towards the sky.