Is it permissible for the person who wants to travel from the United Arab Emirates to Jordan during the day in Ramadan to break his fast before leaving his country; knowing that he had embarked on journey half an hour after dawn?

Praise be to Allah the Lord of the Worlds.

The person who made the intention to embark on journey after dawn must observe fast for that day, because it became an obligation on him before engaging on journey. However, if he experienced unbearable hardship while on travel, then he is permitted to break his fast, but he must make up for the missed day. And Allah The Almighty Knows Best.

Is Zakah(obligatory charity) due on the Zakah money received by a poor person, and reached a Nissab( minimum amount liable for Zakah), and a whole lunar year had lapsed over having it in his possession?

Yes, the poor who possessed a Nissab for a whole lunar year is obliged to pay the Zakah due on that money even if it was given to him as a Zakah money in the first place.

Is it permissible for a woman who is observing `Iddah(waiting period) due to the death of her husband to travel for performing Umrah(Minor Hajj)?

A woman observing `Iddah of a revocable(Rajee`) divorce isn`t allowed to travel for Umrah except with the consent of her husband.

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.