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.
What is the ruling on making up for missed fasting after the second half of Sha`ban (the month before Ramadhaan)?
One is obliged to make up for missed fasting before the start of next Ramadhaan, and regardless of offering it during the first, or the second half of Shab`an. This is because the prohibition mentioned in the Hadith is for offering absolute voluntary fasting in the second half of Sha`ban. And Allah Knows Best.
Is performing Umrah an obligation for who is capable. Is he accountable for not performing it in this case?
Umrah is an obligation once in a lifetime for every Muslim. When physical and financial ability is present, it is preferable to perform Umrah, as well as Hajj. If one can afford to perform Umrah but not Hajj, then they should begin with Umrah, especially since Hajj nowadays is not accessible to everyone who wishes to perform it. In contrast, Umrah is more open and easier to undertake. 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.