Is it permissible to pray for mercy for deceased non-Muslims?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Yes, it is permissible to pray for mercy upon them.
And Allah Almighty knows best.
What is the ruling on the ablution of one who touches his wife without a barrier?
In the Shafi'i school, a man's ablution is invalidated by touching his wife if their skins meet (in any place) without a barrier, whether the touch is intentional or accidental. An exception to this is touching hair, teeth, or nails; these do not invalidate ablution. And Allah the Almighty knows best.
What is the ruling on mentioning Allah`s name upon slaughtering an animal?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is a Sunnah (prophetic tradition) for the person slaughtering to say: "Bismillah" (In the Name of Allah), though the most complete and perfect phrasing is to say: "Bismillah ar-Rahman ar-Rahim" (In the Name of Allah, the Most Gracious, the Most Merciful). This is in accordance with the words of Allah Almighty: "So eat of that [meat] upon which the name of Allah has been mentioned." (Al-An'am/118)
However, pronouncing it is not an obligatory requirement (Wajib). If someone omits it—whether deliberately or out of forgetfulness—the meat remains entirely lawful (Halal) to eat, though purposely omitting it is considered disliked (Makruh). And Allah the Almighty Knows Best.
Is Zakah (obligatory charity) obligatory on indebted merchant?
Debt doesn`t abrogate the dueness of Zakah, thus a debtor who has money, articles of merchandise, or other Zakah funds at his disposal should pay their Zakah.