Bequest for a property to be given to someone after one's death

Q: "A" nominated the name of "BC" in immovable property during his life time at the society records, stating that after his death "BC" will be the owner of the immovable property, in the presence of his other legal heirs/family members and the other legal heirs knows the same, thereafter "A" died, whether the nominees "BC" will be the sole co-owners of the said immovable property or other legal heirs of the deceased will have right over the said property, as per Islam, Please answer.

Binary option trading

Q: Many people are going binary option nowadays to make money. Is it halaal to trade online through investment in binary options in the stock exchange. It basically is speculation whether or not a commodity will go up or down in the stock exchange. Nowadays the software purchased by yourself will do the speculation for you. Please advise whether this sort of earnings in halaal.

Dua after Durood in Salaah

Q: Is the following commonly recited dua after durood thabit?

اللهم اغفرلي و لوالدي و لأستاذي و لجميع المؤمنين و المؤمنات و المسلمين و المسلسلات برحمتك يا أرحم الراحمين

Issuing talaaq on the phone

Q:

1. If a man does not remember that he divorced his wife or not, does talaq takes place?

2. If a man utter the word talaq e.g. usne bola talaq talaq talaq and the wife is on the phone and she heard it? Does talaq takes place in both situations even when the man does not want give her talaq?

Washing impurity from one's clothing

Q: My dress got soiled with stool and while I was washing it, my dress touched my body/thighs before squeezing the water from my dress. Then I continued washing my dress and squeezed it which means my dress is clean now. But this wet dress touched my body/thighs which became naapaak first and I did not wash it because I wanted to wash my dress first. So now did my dress become naapak again? If yes, so how many times should have I washed it - one time or three times? What if I have washed it only once and wore again and sat, slept, etc. Do I need to purify all the things?

Children watching videos in school

Q: I have a question regarding my little brother who is going into a Islamic School in Chicago. He is only 7 years old. In his Islamic school they show kids Islamic/non-Islamic videos of animate objects on the screens, sometimes for educational reasons and sometimes for fun. I know watching these things are not permissible but in his case what should one do to stop this evil? How should this matter be approached?

Also his school has qualified teachers that are teaching there from the Deobandi school of thought. When we can't change their mindset then due to him being only 7 years old, is it permissible to participate in these kind of things. Also we are left with no choice of putting him into any other Islamic school because the situation is much worse and the government wants every child to be in school. If the answers can be mentioned in detail that would be highly appreciated.