Sharing videos of people dancing

Q: Is it permissible to share or to show a video of a group of people (men and women; women are unveiled) all together singing and dancing for a country leader who is not following Islamic laws? I was told that it is okay to share this type of video to others, because it is to show that there are people who are like this.

Is it the duty of the father to support his illegitimate child?

Q: My question is regarding an illegitimate child. My ex husband and I had a child out of wedlock. I was not a Muslim but he was. Before my son was born I embraced Islam. (I was single and not married) Four months after the birth of our son we made nikah. My ex husband has been supporting us as I'm a housewife and we had another child as well. Now that we got divorced my ex husband said that he will no longer pay anything towards the "illegitimate" child. The child carries his name and surname. We were married for almost 8 years. He's also not supporting me financially during my iddat time.

Making wudhu in a place where impurity was washed

Q: I had an infection on my toe which I washed off (whatever was coming out of the infection) in the tub. A little later, while the tub was still wet, I was making wudu in the tub and some water splashed back to me when I washed my face. Was this water impure? Also, when I am filling up a jug to use to make istinja, I sometimes place my finger in the water to check how warm it is. Does this affect the ability of the water to purify?

Women cutting their hair

Q: What is the evidence that women cannot cut their hair? I have searched online for evidence but have not across anything clear. Can a women trim their hair that is below the buttocks (such that it remains still below the buttocks and does not resemble men)?

The root of the hair being impure

Q: I read in Bahisti Zewar under miscellaneous masa'il that if a person uproots his hair, then the root of that hair is regarded as impure because of the stickyness that is found on it.

1. Does this mean that if you uproot a hair anywhere on your body then the root of that hair is impure?

2. If you touch the root of the hair then will your fingers also get impure and do you have to wash your fingers and make wudhu?

3. If you uproot a hair and you touch it but you feel no stickyness then will your fingers become impure?

4. Sometimes I pull at my sideburns and a hair comes out and it is yellowish in colour at the root but when I touch it there is no stickyness on it. Is the root of that hair impure and did my fingers become impure?