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.
Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.
What is the ruling when the duration of the monthly period varies, and sporadically increases?
If the period didn`t exceed (15) days from the first seeing of blood discharges until its end including the times of temporary cessation, then it is menses. But, if the period exceeded (15) days, then the woman experiencing this is Mostahadah (bleeding outside the time of monthly period), and should abide by her regular period, and consult one of the scholars.
What is the ruling on someone who perform their prayer after finishing it because they believe they missed a Rak'a, a prostration, or that they did not perform it correctly (thinking their prayer was invalid)?
If he was sure that his prayer is void then reperforming it is an obligation along with figuring out the reason of invalidity so long as this wasn't out of uncertainty. And Allah Knows Best.