Delaying the Salaah till the last time

Q:

1. I prayed Fajr at about 6:02 and it expires on the calendar at about 6:06, but before I prayed I looked outside and at first I noticed it was light and at the distance I seen in the clouds a reddish smudge, like at the time of Maghrib. Can Fajr expire before the calendar time or is it 100% accurate?

2. I prayed Fajr Qada in-case and at my last rak'ah in tashahhud I didn't have khushoo as I needed to relieve myself, does this affect the validity of my prayer? I leant on one side to hold it and before tasleem I moved back.

Doubts regarding impurity

Q: There was dry blood on my underwear. My hands were wet and I accidently touched it while changing pads. I did not see any visible traces of it on my hand. A drop of water from my wet hands fell on floor but I could not see traces of blood. I accidently stepped on the drop and walked around. Did the house floor get impure?

Removing a poster from the musalla notice board

Q: The 'Al Baraka Bank' had put up a big poster on the note board of a Jamaat Khana. It was a job advertisement, supposedly aimed at the students attending a nearby university. Furthermore, this 'Al Baraka Bank' had hired out a lecture venue at the university. This is for any students wanting to ask questions about the possible career opportunities at the bank etc. The time they set aside for this was between 12:30 and 13:10. When I saw this poster, I was overcome with extreme anger and disgust. When the Jamaat Khana was completely empty, and no one to see me, I removed this poster, tore it up, and threw it in the bin. I am not a trustee of this Jamaat Khana nor do I have any position of authority. If I were to had initially report this poster to the trustees or the Imaam, they would not see anything wrong in this advertising and would not do anything. (1) Since I was not the owner of this evil poster, nor do I have any authority of the Jamaat Khana, was I permitted in discarding the poster? (2) If I acted incorrectly, please advise as to how I can remedy my action.

Making a bequest for a non-heir

Q: My mother passed away 35 years ago my father never remarried. I am his only son and have two elder sisters. My father passed away recently leaving a will which stated that all his household content is to be given to my elder sisters child which is his grandchild. This child also has the first option to buy his house at market price. He has 15 other grandchildren. This has split the family as a grandchild may not inherit from him. The money from the sale of his house is to be divided equally between his three children. Can you please give advise as to the right way things should be done.

Tawbah

Q: If a female who is menstruating makes a mistake and cannot pray the prayer of repentance so she repents in her heart by asking for forgiveness and saying sorry and at the end says ameen, does it count or do you have to read /say something a surah or something in the beginning as well?