I suffer from absentmindedness and constant worries during prayer, what should I do?
You should take refuge in Allah from the whispers of the devil and life worries. You should also seek Allah`s help and offer a lot of Istigfar (seeking the forgiveness of Allah). And Allah Knows Best.
What is the Ruling on Reciting the Prophetic Narration?
All Perfect Praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.
Reciting the Prophetic narration is permissible as many scholars used to, since in principle, the rulings of recitation have to be observed while speaking Arabic language. And Allah Knows Best.
Is it permissible to pray with a heater (stove) in front of me?
There is no harm in praying with a heater in front of you, as long as you do not intend to venerate the fire or imitate those who worship it. And Allah Knows Best.
Is it permissible to recite the Holy Qur'an or to play a recording at mourning gatherings? Or is it considered an innovation?
Whenever Qur'anic verses are recited, it is obligatory upon everyone to listen, otherwise; they should remain silent. And Allah Knows Best.