Is it permissible for a person who had vowed to give a certain amount of money to another, but didn`t find the latter to donate that money to the mosque?

In principle, the vowing person should abide by his vow as much as possible. Therefore, if he couldn`t find the person that he had made the vow for, then the vow itself is countless and nothing is due on its maker. However, if the latter happens to find the former later on then, he has to give him that money.

Is it permissible for a person to sever ties with his sister because her husband had quit prayer and done him harm?

A sister is a blood-relative and maintaining blood-relations is obligatory in Islam. As regards her husband, he should be invited to the way of Allah with wisdom and beautiful preaching.

 Should a person who doesn’t offer Tasbeehb (saying Subhaana Rabbiya Al-‘Atheem during Rukoo`, and saying Subhaana Rabbiya Al-A‘laa during Sujood) during Rukoo` and Sujood perform As-Sahw Sujood (prostration of forgetfulness)?

He/ she doesn`t have to perform Sujood As-Sahw, whether he/she didn`t offer Tasbeeh during Rukoo` and Sujood either intentionally ,or unintentionally, provided that the attentiveness of the heart wasn`t undermined since it is a pillar in both.

What is the ruling on performing voluntary prayers during official working hours?

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

There is no harm if  there was break time during official working hours, but if not then it is impermissible. And Allah Knows Best.