Yes, tahajjud is a time for the acceptance of duas, akhi.
However, when you make dua to Allah swt, He may not answer it in the way you expect. He may delay something for a good reason, or give you something in its place which is of even greater benefit, or you may receive the rewards in the Hereafter. The key is not to be impatient, Allah swt is the best of Planners, He knows what is best for you better than you know yourself.
But yes, you must always make dua, and definitely wake up for Tahajjud, once you get into the habit, is the *most* amazing feeling *ever*. Such a special time to worship your Rabb and you can so feel it subhanAllah.
Here are some hadiths about tahajjud:
Abu Hurairah reports that the Messenger of Allah (saws) said: “Our Lord Descends to the lowest heaven during the last third of the night, inquiring: `Who will call on Me so that I may respond to him? Who is asking something of Me so I may give it to him? Who is asking for My forgiveness so I may forgive him?”[ Bukhari and Muslim.]
Abdullah ibn `Amr reports that the Prophet (saws) said: “The most beloved fast to Allah is the fast of (Prophet) Dawood (a.s.). And the most beloved prayer to Allah is the prayer of (Prophet) Dawood (a.s.). He (Prophet Dawood (a.s.)) would sleep half of the night and then pray during the next third of the night and then sleep during the last sixth of the night.And he would fast one day and not fast the next.”[ Bukhari and Muslim.]
Abu Hurayra (Allah be pleased with him) reports that the Messenger of Allah (blessings and peace be upon him, his family, and companions) said, “The best prayer after the obligatory prayers is the night prayer.”[Muslim]
Abd Allah ibn Salam (Allah be pleased with him) reports that the Messenger of Allah (blessings and peace be upon him, his family, and companions) said, “O people! Spread the salams, feed others, maintain family ties, and pray at night when others sleep and you will enter Heaven safely.”[Tirmidhi, Hakim]