Is it permissible to offer mandatory prayer while sitting?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions. Standing up is a pillar in the mandatory prayer and the prayer is not valid without it unless one cannot do it. As for Nafila (supererogatory prayer), one can perform it in the state of sitting even if he/she can stand, but his/her reward is half the reward of the person who prays while standing if he/sh has no legal excuse for such an act. And Allah Knows Best.
Is the father a Mahram (Non-marriageable) to his son`s mother-in-law?
The father is a non-Mahram (Marriageable) to his son`s mother-in-law, so it is impermissible for them to look at each other, or to have a seclusion (Khalwah).
1- A young man whose father and grandfather are dead. Unfortuntly, he passedaway leaving a mother, two sisters and a brother. Do his paternal uncles inherit him? 2- A man died leaving daughters, a wife, brothers, a mother or no mother. It is well known that the daughters inherit two thirds and the wife one eighth. To whom does the rest of the estate go and what is the evidence on that from the texts of Sharia?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
1- The full brother or the paternal half-sibling disinherits the paternal uncles. The paternal half-sibling takes one sixth and because they are from the Asabah (Male relatives on the father`s side) of the deceased they take the rest of the estate. The proof of this is that Ibn ‘Abbas (May Allah Be Pleased with them) reported God’s Messenger (PBUH) as saying: "Give the shares to those who are entitled to them, and what remains over goes to the nearest male heir." [Agreed upon]. In this case, nothing is left to them.
2- The brothers take the rest of the deceased`s estate and the full brother disinherits the paternal half-sibling, and the proof of this is the aforementioned narration. And Allah The Almighty 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.