What is the expiation for breaking fast due to being on a journey, or being sick, or being in a state of menstruation?

No expiation is due on the aforesaid categories, but they are obliged to make up for the missed fast. However, if any of them failed to do so while being able to, and the next Ramadhaan has come, then making up for those days is incumbent on him/her , and paying the ransom as well.

Is it permissible for a woman to sit with her brothers –in- law?

It is impermissible for a woman to sit with her brothers-in-law, and it is also impermissible for a person to have a Khulwa(seclusion) with his sister-in-law.

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 mandatory in Islam. As regards her husband, he should be invited to the way of Allah with wisdom and beautiful preaching.

What are the benefits of slaughtering an Aqeeqah?

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.

Extending thanks to Allah for His grace, expressing happiness for having a newborn, declaring lineage, and feeding the mother to compensate for the blood that she had lost during delivery.