In the last verse of Surah At-Tin, Allah Says (What means): "Is Allah not the most just of judges?" [At-Tin/8]. Is it permissible for us, while performing congregational prayer, to respond after the Imam recites it by saying: "Indeed, and I am among those who bear witness to that." ?
It is recommended for the worshipper to say 'Indeed' (Bala) silently after reciting or hearing the verse (/What means): "Is Allah not the most just of judges?" [At-Tin/8]. This is part of reflecting on the Quran during its recitation or listening, as Allah Says (What means): "Then do they not reflect upon the Quran, or are there locks upon [their] hearts?" (Muhammad: 24). Doing so helps in achieving humility and focus in prayer. And Allah Knows Best
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 conclude her marriage without the approval of her family?
No marriage is permissible without the presence of a guardian and two trust worthy witnesses, and the woman whose family had denied her right in getting married to a God-fearing, financially and physically capable man should go to the court.
What is the best manner in distributing the meat of the Aqeeqah?
It is better to divide all of it as cooked meat amongst the poor and the needy. Dividing it into three portions is a Sunnah, but it is permissible to keep all of it provided that a portion, even a small one, is given to the poor and needy (one kilo for example).