Summarized Fatawaa
• Is it permissible for the doctor to uncover the hair of a female patient out of necessity?
It is only permissible for him to do so when there is no female doctor, and he should examine the patient in the presence of one of her Mahrams(unmarriageable kin).
• After I had prayed, I found a drop of menstrual blood and was unsure when that happened; what is the ruling on my prayer and fast?
All praise is due to Allah, peace and blessing be upon the Messenger of Allah: Your prayer and fast are correct , and you should not make up for them, and we ask Allah, The Almighty, to duely reward you for these acts of worship. Your menses start once you see blood because the situation remains as such unless there is certainty or predominant conjecture, as per the Fiqh maxim: 'Certainty is not removed by doubt'. And Allah knows best.
• Is it permissible for a woman to shake hands with her brother-in-law?
It is forbidden for the woman to shake hands with her brother-in-law because he isn`t a Mahram(unmarriageable) of hers.
• 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 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(Prostration of forgetfulness).