Witr and Nawaafil

Is it permissible to perform the Sunnats of fajr after the fajr Salaah?

Q: I woke up for fajr and thought there was not enough time to read the sunnahs, so I read the fard. After completing the fard, I realized there was still time left, so I read the sunnahs of Fajr after praying the fard of Fajr, within the time of Fajr. are the sunnahs valid? Or will I need to redo them after sunrise?

Tahajjud Salaah

Q: It is mentioned in the Hadith that Voluntary Worship is a means of attaining proximity to Allah. Besides the Obligatory and Essential Prayers, the Holy Prophet (Sallallahu Alayhi Wasallam) used to make arrangements for the Voluntary (Nawafil) Prayers too.

1) I want to perform tahajjud namaz daily but when I sleep I don't wake up at the time of tahajjud. So can I just offer eight rakats Voluntary Worship for Allah before going to sleep daily?

2) Is it allowed to perform extra Voluntary Worship any time of a day and any time of night before going to sleep?

Delaying the witr Salaah

Q: My question is about witr Salaah:

1. After performing Esha Sallah at 8.00pm, can I delay my Witr Salaah till 11.00 pm(my sleep time)?

2. Can I combine Tahajjad and witr at the above mentioned time?

3. What will be my last Salaah before I go to sleep, Tahajjad or witr?