Re: dua during the last third of the night...
Xclusive, here is an ahadith i found in this regard:
Hadith Qudsi 35:
On the authority of Abu Hurayrah (Radhi Allahu Ta'ala Anhu), who said that the Messenger of Allah (Sall Allahu alaihi wa Aalihi wa Sallim) said:
Our Lord (glorified and exalted be He) descends each night to the earth's sky when there remains the final third of the night, and He says: Who is saying a prayer to Me that I may answer it? Who is asking something of Me that I may give it him? Who is asking forgiveness of Me that I may forgive him?
It was related by al-Bukhari (also by Muslim, Malik, at-Tirmidhi and Abu Dawud). In a version by Muslim the Hadith ends with the words: And thus He continues till [the light of] dawn shines.
Wassalam