What should a worshiper who has forgotten a pillar of prayer do?
If he/she remembered the forgotten pillar before offering it in the following Rakah (unit of prayer), then he/she should offer it, and continue the prayer, then offer Sujood As-Sahw (Prostration of forgetfulness) at the end of it. But, if he/she remembered that forgotten pillar after having offered it in the following Rakah, then he/she should offer a new Rakah in its (the one in which he forgot a pillar) place, and offer Sujood As-Sahw.
Is it permissible for a person who hasn`t made ablution to call for prayer (Adhan)?
All perfect praise be to Allah, The Lord of The Worlds. It is disliked for a person with a minor impurity to call for prayer, but if he does , then it`s valid and sufficient. And Allah Knows Best.
I have a question regarding the deferred portion of the dowry (Mahr)*. Is the wife entitled to it only upon divorce or she can claim it even if divorce hasn`t taken place? Moreover, does she have the right to claim this portion after death of husband, even if he didn`t divorce her before that?
All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
In the marriage contract, it is recorded that the deferred portion of the dowry is due upon divorce or death, whatever comes first. If divorce took place first then the woman is entitled to it and if the husband died this amount must be paid from his estate. On the other hand, if the woman died then the husband becomes liable for this portion and it becomes part of the woman`s estate. We advise every husband to give this portion to his wife while alive because it is a right of hers. And Allah The Almighty Knows Best.
* In Islam, a Mahr is the obligation, in the form of money or possessions paid by the groom, to the bride at the time of Islamic marriage (payment also has circumstances on when and how to pay). While the mahr is often money, it can also be anything agreed upon by the bride such as jewelry, home goods, furniture, a dwelling or some land. Mahr is typically specified in the marriage contract signed upon marriage.
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.