Is it permissible to offer Salah (prayer) on behalf of the sick who is on his/her death bed, and is incapable of offering it?
It`s impermissible to offer Salah on behalf of the sick, or the dead.
A man who was on travel prayed Duhr as four Rakhas upon leaving Tafilah heading to Amman. However, on his way to Amman, he prayed Asir as two Rakhas (Shortened). Is what he did correct from an Islamic perspective?
All perfect praise be to Allah, The Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
What he did is correct; he is liable for nothing before Allah The Almighty, since combining and shortening prayers during travel are two separate concessions. Therefore, it is permissible for a traveler to shorten prayer without combining it with another. And Allah The Almighty Knows Best.
I work in an accounting and auditing office, and among the clients of the office are restaurants, hotels, and supermarkets that sell alcohol. Our work is limited to collecting invoices, whether purchases, sales, or expenses, and recording them in daily books. We also review income and sales taxes on behalf of these clients.
You are more knowledgeable about the nature of your work. If you see it as assisting in wrongdoing, then it is forbidden, as Allah The Exalted Says (What means): "And cooperate in righteousness and piety, but do not cooperate in sin and aggression" [Al-Ma’idah/2]. However, if your work is merely documenting the reality, then I hope there is no sin upon you. The the pious predecessors (Salaf) used to take the tithe from the traders of the People of the Book, even if it included alcohol, after knowing the value of their goods. And Allah The Almighty Knows Best.
Is it permissible for a person who broke fasting in Ramadan because of being sick to pay a ransom?
If there is hope for him/her to be cured, then he would be required to make up for the missed fasting days when he/she recovers, and no ransom is due on him/her. If his/her disease is incurable, then he/she would be required to pay a ransom for each missed fasting day, which is (600) grams of wheat, or rice. And Allah Knows Best.