is it allowed to pray any prayer after prayed witr and before fajr like nafila or qadha-prayer or should witr be the last prayer?
2. Could one pray tahajjud/ witr after waking up even if the time of fajr already has entered (but obviously there is still enough time to pray witr, sunnah of fajr and fajr)? I have heard that would be permissible as a rukhsa.
Yes it is permissible, although witr should ideally be the last prayer. If you have already prayed witr, then wish to pray more, then there is no harm.
In the Hanbali madhhab the time for witr ends at the start of Fajr, because this was reported in some Prophetic narrations as the end time of witr, so you should not pray witr after Fajr times has started. There is scope for doing it according to Imam Malik and other scholars, but the position of the madhhab does not allow that. Instead, you would make up the witr prayer after sunrise.
This answer was collected from The Hanbali Madhhab website. The answers to the questions are given by Imam Zahed Fattah in accordance to the Hanbali School of Jurisprudence.