Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
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 buying shares from the Arab Bank permissible?
Buying and selling shares owned by usrious companies is impermissble. And Allah Knows Best.
What is the ruling on eating the food prepared by Christians friends knowing that their income comes from trading in alcoholic drinks?
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.
It isn`t allowed to have the food of the person whose source of income is unlawful. However, if it is a mixture of lawful and unlawful, then it is permissible to have their food. And Allah The Almighty Knows Best.