Is it permissible for a woman to sit with her brothers-in-law?
It is impermissible for a woman to sit with her brothers-in-law, and it is also impermissible for a person to have a Khulwa (seclusion) with his sister-in-law.
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 to single out Fridays, Saturdays, and Sundays to make up for missed fasting without fasting a day before ,or after each ?
Yes, it is permissible to make up for missed fasting during the aforesaid days, and it is also valid to offer non-obligatory and vowed fasting as well. However, fasting a day before or after each isn`t obligatory. And Allah Knows Best.
After I was ran over, I had cracked ribs, concussion, a tension pneumothorax, and retired as a result. What is the amount of the Diya?
All praise is due to Allah the Lord of the worlds. May the blessings of Allah be upon our Master and Prophet Muḥammad and his pure progeny.
What you have mentioned requires a detailed medical report since the benefit of every organ that you have lost deserves a full Diya (In Islamic law, Diya is the financial compensation paid to the victim or heirs of a victim in the cases of accidental murder, bodily harm or property damage). Moreover, the decrease in the benefit of some organs has to be assessed by expert doctors and allocated a percentage from the Diya accordingly. Therefore, we advise you to refer the matter to the courts or reconcile with the driver and forgive him so that Allah may forgive you. And Allah The Almighty Knows Best.