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.
If someone starts the day sick or traveling while fasting, is it permissible for them to break their fast?
● A sick person who finds fasting difficult is allowed to break their fast, whether they began the day fasting or not.
● As for a traveler:
○ If they were still at home at dawn and then traveled after Fajr (dawn), they must continue fasting unless they experience extreme hardship, in which case they may break their fast.
○ However, if they were already traveling when dawn broke—meaning they had left their town before Fajr—then they are permitted to break their fast. This is what the Prophetﷺ did during the year of the conquest (of Makkah).
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
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.