Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
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
Is it permissible for a woman to say that she loves her husband more than her father?
It is impermissible for her to say so since this would hurt her father deep down. Allah, The Almighty, Says in this regard (What means): "And that ye be kind to parents." [Al-Isra/23]. Saying such a thing to her father isn`t an act of kindness since she should keep it to herself even if she felt that way.
Is it permissible to combine and shorten prayers at home before traveling?
It is impermissible to combine and shorten prayers at home before traveling because a person is called a traveler once he/she departs the borders of his/her country, and offering prayer that way was originally intended to exempt a traveler. And Allah Knows Best.