Is performing Umrah an obligation for who is capable. Is he accountable for not performing it in this case?
Umrah is an obligation once in a lifetime for every Muslim. When physical and financial ability is present, it is preferable to perform Umrah, as well as Hajj. If one can afford to perform Umrah but not Hajj, then they should begin with Umrah, especially since Hajj nowadays is not accessible to everyone who wishes to perform it. In contrast, Umrah is more open and easier to undertake. And Allah knows best.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. 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
Is it permissible for the mother to offer an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)for her son?
Aqeeqah is due on the one obliged to provide for the newborn, and it is permissible for the grandfather, or the mother to offer the Aqeeqah.