What is the ruling on giving my mother a gift at "Mother's day", is it Halal or Haram?
Praise be to Allah the Lord of the Worlds.
There is nothing wrong with doing that as long as it isn`t done in imitation of the disbelievers. And Allah The Almighty Knows Best.
Is it permissible to offer Tahajjud prayer after Witr prayer?
It is permissible to offer voluntary prayer after Witr (An odd number prayer performed between Isha and Fajr) prayer. However, it is desirable that the night prayer be ended with Witr. Therefore, it is desirable for one, who thought that he was most probably going to wake up at night in order to offer Tahajjud, to offer Witr after it, but one, who fears that he might not wake up, should offer Witr before going to bed.
I took a car from the Orphans' Fund Development Institution; is there usury (Riba) involved in this transaction?
If the Sharia's conditions were met, then there is no harm in this. And Allah The Exalted Knows Best.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.