Can a woman perform I‘tikaf in her home?
No, a woman's I‘tikaf is not valid if performed at home, because her home is not a mosque.
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.
Is it permissible to authorize charitable organizations to perform the Udhiyah on one`s behalf?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to authorize charitable organizations to perform the sacrifice (Udhiyah) on one’s behalf. However, if these organizations undertake the slaughtering for a group of people, those in charge of the slaughtering must maintain lists of the names of those who authorized them. Furthermore, at the time of slaughter, the slaughterer must intend that the specific sacrifice is on behalf of a specific person. And Allah the Almighty knows best.
How to pay Zakah (obligatory charity) due on articles of merchandise?
Articles of merchandise are estimated by their whole sale market price at the end of each lunar year, and (2.5%) of their value is paid as Zakah whether it (value) went up, or down compared to actual purchasing price, and whether the increase (profit) was in the article itself such as an increase in the animal`s weight, or in the prices themselves. And Allah Knows Best.