Is it permissible for one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram (Marriageable) to her.
A woman is asking for divorce although she is still breastfeeding. What is the Islamic ruling on this?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
It unlawful for a woman to seek divorce without a valid Sharia excuse. And Allah The Almighty Knows Best.
Is it permissible for a Muslim woman to wear trousers at home?
Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. And Allah Knows Best.
What is the ruling of Sharia on unregistered marriage in Jordan?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Aishah narrated that the Messenger of Allah said: "Whichever woman married without the permission of her Wali her marriage is invalid, her marriage is invalid, her marriage is invalid. If he entered into her, then the Mahr is for her in lieu of what he enjoyed from her private part. If they disagree, then the Sultan is the Wali for one who has no Wali." [At-Tirmithi, Hadith No.1102]. The Prophet (PBUH) also said: "There is no marriage without a guardian and two honorable witnesses." Related in [Al-Mo`jam Al-Basit for At-Tabarani, pp.6366]. Registration of the marriage contract at Islamic court is necessary for the preservation of rights and failing to do so is punishable by Jordanian Law. And Allah The Almighty Knows Best